slope-analysis-longest-spatial.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pickle\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import utils\n",
    "def run_extremes(N, W, pmf_cust, pmf_serv, gurobi_flag = 0):\n",
    "    Ex = round (np.sum(np.outer(pmf_cust,pmf_serv)*W), 3) \n",
    "    print(\"Expected cost for c = 0 case:\", Ex )\n",
    "    if gurobi_flag == 1:\n",
    "        fluid_sol = utils.fluid_solution_gurobi(N, W, pmf_cust, pmf_serv)\n",
    "    else:\n",
    "        fluid_sol = utils.fluid_solution(N, W, pmf_cust, pmf_serv,0)\n",
    "#     print(\"\\nFluid Solution:\\n\")\n",
    "#     print(fluid_sol)\n",
    "    return([Ex,fluid_sol])\n",
    "def plot_from_sim_paths(file_name, save_file= 0, frac = 0):\n",
    "    with open(file_name,'rb') as f:\n",
    "        M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "    Q_paths_M = M_res[\"Q_paths\"]\n",
    "    C_paths_M = M_res[\"C_paths\"]\n",
    "    Q_paths_B = B_res[\"Q_paths\"]\n",
    "    C_paths_B = B_res[\"C_paths\"]\n",
    "    (average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M, frac)\n",
    "    (average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B, frac)\n",
    "    [Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)\n",
    "    utils.qc_plot(Ex,fluid_sol,average_queue_B,average_cost_B,average_queue_M,average_cost_M, save_file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 3.857\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
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      "  2.23606798 2.82842712 3.60555128 4.47213595 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.         5.65685425 5.38516481 5.09901951 5.38516481 5.83095189\n",
      "  6.40312424]\n",
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      "  3.16227766 3.60555128 4.24264069 5.         4.47213595 4.12310563\n",
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      "  5.83095189]\n",
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      "  3.60555128 2.82842712 2.23606798 2.82842712 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 5.65685425 5.         4.47213595\n",
      "  4.12310563 4.47213595 6.40312424 5.83095189 5.38516481 5.09901951\n",
      "  5.38516481]\n",
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      "  4.47213595 3.60555128 2.82842712 2.23606798 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 6.40312424 5.65685425 5.\n",
      "  4.47213595 4.12310563 7.07106781 6.40312424 5.83095189 5.38516481\n",
      "  5.09901951]\n",
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      "  2.23606798 3.16227766 4.12310563 5.09901951 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 3.16227766 3.60555128 4.24264069\n",
      "  5.         5.83095189 4.12310563 4.47213595 5.         5.65685425\n",
      "  6.40312424]\n",
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      "  1.41421356 2.23606798 3.16227766 4.12310563 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
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      "  2.23606798 1.41421356 2.23606798 3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.24264069 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.        ]\n",
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      "  2.82842712 2.23606798 2.82842712 5.         4.24264069 3.60555128\n",
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      "  3.16227766 4.12310563 5.09901951 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 3.16227766 3.60555128 4.24264069 5.\n",
      "  5.83095189]\n",
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      "  2.23606798 3.16227766 4.12310563 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.60555128 3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
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      "  1.41421356 2.23606798 3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.24264069 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069]\n",
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      "  3.60555128 2.82842712 2.23606798 2.82842712 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 5.         4.24264069 3.60555128 3.16227766\n",
      "  3.60555128]\n",
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      "  4.47213595 3.60555128 2.82842712 2.23606798 5.09901951 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.83095189 5.         4.24264069 3.60555128\n",
      "  3.16227766]\n",
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      "  3.60555128 3.16227766 3.60555128 4.24264069 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 3.60555128 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.47213595 5.\n",
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      "  3.60555128 2.82842712 2.23606798 5.09901951 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 5.38516481 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798]\n",
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      "  4.47213595 5.         5.65685425 6.40312424 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 1.41421356 2.23606798 3.16227766 4.12310563\n",
      "  5.09901951]\n",
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      "  3.60555128 4.24264069 5.         2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 2.23606798 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
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      "  5.65685425 5.         4.47213595 4.12310563 5.83095189 5.\n",
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      "  1.41421356]]\n"
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    {
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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "file_name = \"../longest_spatial_uniform_25_all_good.pkl\"\n",
    "plot_from_sim_paths(file_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 3.857\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
      " [2.23606798 1.41421356 2.23606798 3.16227766 4.12310563 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.         5.65685425 5.38516481 5.09901951 5.38516481 5.83095189\n",
      "  6.40312424]\n",
      " [3.16227766 2.23606798 1.41421356 2.23606798 3.16227766 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         4.47213595 4.12310563\n",
      "  4.47213595 5.         5.83095189 5.38516481 5.09901951 5.38516481\n",
      "  5.83095189]\n",
      " [4.12310563 3.16227766 2.23606798 1.41421356 2.23606798 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 5.65685425 5.         4.47213595\n",
      "  4.12310563 4.47213595 6.40312424 5.83095189 5.38516481 5.09901951\n",
      "  5.38516481]\n",
      " [5.09901951 4.12310563 3.16227766 2.23606798 1.41421356 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 6.40312424 5.65685425 5.\n",
      "  4.47213595 4.12310563 7.07106781 6.40312424 5.83095189 5.38516481\n",
      "  5.09901951]\n",
      " [2.23606798 2.82842712 3.60555128 4.47213595 5.38516481 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 5.09901951 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 3.16227766 3.60555128 4.24264069\n",
      "  5.         5.83095189 4.12310563 4.47213595 5.         5.65685425\n",
      "  6.40312424]\n",
      " [2.82842712 2.23606798 2.82842712 3.60555128 4.47213595 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
      " [3.60555128 2.82842712 2.23606798 2.82842712 3.60555128 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.24264069 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.        ]\n",
      " [4.47213595 3.60555128 2.82842712 2.23606798 2.82842712 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 2.23606798 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 5.65685425 5.         4.47213595 4.12310563\n",
      "  4.47213595]\n",
      " [5.38516481 4.47213595 3.60555128 2.82842712 2.23606798 5.09901951\n",
      "  4.12310563 3.16227766 2.23606798 1.41421356 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.83095189 5.         4.24264069\n",
      "  3.60555128 3.16227766 6.40312424 5.65685425 5.         4.47213595\n",
      "  4.12310563]\n",
      " [3.16227766 3.60555128 4.24264069 5.         5.83095189 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 5.09901951 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 3.16227766 3.60555128 4.24264069 5.\n",
      "  5.83095189]\n",
      " [3.60555128 3.16227766 3.60555128 4.24264069 5.         2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.60555128 3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
      " [4.24264069 3.60555128 3.16227766 3.60555128 4.24264069 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.24264069 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069]\n",
      " [5.         4.24264069 3.60555128 3.16227766 3.60555128 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 5.         4.24264069 3.60555128 3.16227766\n",
      "  3.60555128]\n",
      " [5.83095189 5.         4.24264069 3.60555128 3.16227766 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.09901951 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.83095189 5.         4.24264069 3.60555128\n",
      "  3.16227766]\n",
      " [4.12310563 4.47213595 5.         5.65685425 6.40312424 3.16227766\n",
      "  3.60555128 4.24264069 5.         5.83095189 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563 5.09901951 2.23606798 2.82842712 3.60555128 4.47213595\n",
      "  5.38516481]\n",
      " [4.47213595 4.12310563 4.47213595 5.         5.65685425 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 2.82842712 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595]\n",
      " [5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.24264069 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 3.60555128 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  4.24264069 3.60555128 3.16227766 3.60555128 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 4.47213595 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712]\n",
      " [6.40312424 5.65685425 5.         4.47213595 4.12310563 5.83095189\n",
      "  5.         4.24264069 3.60555128 3.16227766 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.09901951 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 5.38516481 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798]\n",
      " [5.09901951 5.38516481 5.83095189 6.40312424 7.07106781 4.12310563\n",
      "  4.47213595 5.         5.65685425 6.40312424 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 1.41421356 2.23606798 3.16227766 4.12310563\n",
      "  5.09901951]\n",
      " [5.38516481 5.09901951 5.38516481 5.83095189 6.40312424 4.47213595\n",
      "  4.12310563 4.47213595 5.         5.65685425 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 2.23606798 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
      " [5.83095189 5.38516481 5.09901951 5.38516481 5.83095189 5.\n",
      "  4.47213595 4.12310563 4.47213595 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 3.16227766 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766]\n",
      " [6.40312424 5.83095189 5.38516481 5.09901951 5.38516481 5.65685425\n",
      "  5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 4.12310563 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798]\n",
      " [7.07106781 6.40312424 5.83095189 5.38516481 5.09901951 6.40312424\n",
      "  5.65685425 5.         4.47213595 4.12310563 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.09901951 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356]]\n"
     ]
    }
   ],
   "source": [
    "with open(\"../longest_spatial_uniform_25_all_good.pkl\",'rb') as f:\n",
    "    M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "Q_paths_M = M_res[\"Q_paths\"]\n",
    "C_paths_M = M_res[\"C_paths\"]\n",
    "Q_paths_B = B_res[\"Q_paths\"]\n",
    "C_paths_B = B_res[\"C_paths\"]\n",
    "(average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M, 0)\n",
    "(average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B, 0)\n",
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"../longest_spatial_uniform_25_more_3_ig.pkl\",'rb') as f:\n",
    "    M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "Q_paths_M = M_res[\"Q_paths\"]\n",
    "C_paths_M = M_res[\"C_paths\"]\n",
    "Q_paths_B = B_res[\"Q_paths\"]\n",
    "C_paths_B = B_res[\"C_paths\"]\n",
    "(average_cost_M2, average_queue_M2) = utils.average_paths(C_paths_M,Q_paths_M, 0)\n",
    "(average_cost_B2, average_queue_B2) = utils.average_paths(C_paths_B,Q_paths_B, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 598.9,  698.1,  797.3,  896.5, 1000.5, 1094.5, 1194.1])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.0000000e+00, 1.5000000e+00, 1.9999900e+00, 2.5000000e+00,\n",
       "       3.0000000e+00, 4.5000000e+00, 5.5000000e+00, 6.4998400e+00,\n",
       "       7.9997500e+00, 9.4996000e+00, 1.0500000e+01, 1.5499000e+01,\n",
       "       2.0500000e+01, 2.5500000e+01, 3.0496000e+01, 5.0500000e+01,\n",
       "       6.7982500e+01, 7.5475000e+01, 1.0050000e+02, 1.2550000e+02,\n",
       "       1.5040000e+02, 1.6288750e+02, 1.7537500e+02, 2.0050000e+02,\n",
       "       2.2532500e+02, 2.3771875e+02, 2.5050000e+02, 2.7527500e+02,\n",
       "       3.0010000e+02, 3.2522500e+02, 3.5020000e+02, 5.9890000e+02,\n",
       "       6.9810000e+02, 7.9730000e+02, 8.9650000e+02, 1.0005000e+03,\n",
       "       1.0945000e+03, 1.1941000e+03])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 3.857\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
      " [2.23606798 1.41421356 2.23606798 3.16227766 4.12310563 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.         5.65685425 5.38516481 5.09901951 5.38516481 5.83095189\n",
      "  6.40312424]\n",
      " [3.16227766 2.23606798 1.41421356 2.23606798 3.16227766 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         4.47213595 4.12310563\n",
      "  4.47213595 5.         5.83095189 5.38516481 5.09901951 5.38516481\n",
      "  5.83095189]\n",
      " [4.12310563 3.16227766 2.23606798 1.41421356 2.23606798 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 5.65685425 5.         4.47213595\n",
      "  4.12310563 4.47213595 6.40312424 5.83095189 5.38516481 5.09901951\n",
      "  5.38516481]\n",
      " [5.09901951 4.12310563 3.16227766 2.23606798 1.41421356 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 6.40312424 5.65685425 5.\n",
      "  4.47213595 4.12310563 7.07106781 6.40312424 5.83095189 5.38516481\n",
      "  5.09901951]\n",
      " [2.23606798 2.82842712 3.60555128 4.47213595 5.38516481 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 5.09901951 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 3.16227766 3.60555128 4.24264069\n",
      "  5.         5.83095189 4.12310563 4.47213595 5.         5.65685425\n",
      "  6.40312424]\n",
      " [2.82842712 2.23606798 2.82842712 3.60555128 4.47213595 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
      " [3.60555128 2.82842712 2.23606798 2.82842712 3.60555128 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.24264069 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.        ]\n",
      " [4.47213595 3.60555128 2.82842712 2.23606798 2.82842712 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 2.23606798 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 5.65685425 5.         4.47213595 4.12310563\n",
      "  4.47213595]\n",
      " [5.38516481 4.47213595 3.60555128 2.82842712 2.23606798 5.09901951\n",
      "  4.12310563 3.16227766 2.23606798 1.41421356 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.83095189 5.         4.24264069\n",
      "  3.60555128 3.16227766 6.40312424 5.65685425 5.         4.47213595\n",
      "  4.12310563]\n",
      " [3.16227766 3.60555128 4.24264069 5.         5.83095189 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 5.09901951 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 3.16227766 3.60555128 4.24264069 5.\n",
      "  5.83095189]\n",
      " [3.60555128 3.16227766 3.60555128 4.24264069 5.         2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.60555128 3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
      " [4.24264069 3.60555128 3.16227766 3.60555128 4.24264069 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.24264069 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069]\n",
      " [5.         4.24264069 3.60555128 3.16227766 3.60555128 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 5.         4.24264069 3.60555128 3.16227766\n",
      "  3.60555128]\n",
      " [5.83095189 5.         4.24264069 3.60555128 3.16227766 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.09901951 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.83095189 5.         4.24264069 3.60555128\n",
      "  3.16227766]\n",
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      "  3.60555128 4.24264069 5.         5.83095189 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563 5.09901951 2.23606798 2.82842712 3.60555128 4.47213595\n",
      "  5.38516481]\n",
      " [4.47213595 4.12310563 4.47213595 5.         5.65685425 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 2.82842712 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595]\n",
      " [5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.24264069 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 3.60555128 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  4.24264069 3.60555128 3.16227766 3.60555128 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 4.47213595 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712]\n",
      " [6.40312424 5.65685425 5.         4.47213595 4.12310563 5.83095189\n",
      "  5.         4.24264069 3.60555128 3.16227766 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.09901951 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 5.38516481 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798]\n",
      " [5.09901951 5.38516481 5.83095189 6.40312424 7.07106781 4.12310563\n",
      "  4.47213595 5.         5.65685425 6.40312424 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 1.41421356 2.23606798 3.16227766 4.12310563\n",
      "  5.09901951]\n",
      " [5.38516481 5.09901951 5.38516481 5.83095189 6.40312424 4.47213595\n",
      "  4.12310563 4.47213595 5.         5.65685425 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 2.23606798 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
      " [5.83095189 5.38516481 5.09901951 5.38516481 5.83095189 5.\n",
      "  4.47213595 4.12310563 4.47213595 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 3.16227766 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766]\n",
      " [6.40312424 5.83095189 5.38516481 5.09901951 5.38516481 5.65685425\n",
      "  5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 4.12310563 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798]\n",
      " [7.07106781 6.40312424 5.83095189 5.38516481 5.09901951 6.40312424\n",
      "  5.65685425 5.         4.47213595 4.12310563 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.09901951 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356]]\n"
     ]
    },
    {
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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_from_sim_paths(\"../longest_spatial_uniform_25_more_3_ig.pkl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2d60ab03cf8>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.log(average_cost_M), np.log(average_queue_M), 'go')\n",
    "plt.plot(np.log(average_cost_B), np.log(average_queue_B), 'bx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2d65f0b94e0>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(average_cost_M, np.log(average_queue_M), 'go')\n",
    "plt.plot(average_cost_B, np.log(average_queue_B), 'bx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2d632f15400>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.log(average_cost_M), (average_queue_M), 'go')\n",
    "plt.plot(np.log(average_cost_B), (average_queue_B), 'bx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the sorted indices of x\n",
    "sorted_indices = np.argsort(average_cost_B)\n",
    "\n",
    "# Sort x and reorder y accordingly\n",
    "average_cost_B = average_cost_B[sorted_indices]\n",
    "average_queue_B = average_queue_B[sorted_indices]\n",
    "\n",
    "# Get the sorted indices of x\n",
    "sorted_indices = np.argsort(average_cost_M)\n",
    "\n",
    "# Sort x and reorder y accordingly\n",
    "average_cost_M = average_cost_M[sorted_indices]\n",
    "average_queue_M = average_queue_M[sorted_indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-31.53262772  17.3605827 ] [0.28169313]\n",
      "[-16.84457596  13.30140714] [0.57174811]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2d60935d4e0>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM = np.log(average_cost_M[:15])\n",
    "yM = np.log(average_queue_M[:15])\n",
    "xB = np.log(average_cost_B[:23])\n",
    "yB = np.log(average_queue_B[:23])\n",
    "\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM, yM, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM, yM,'go',markersize = 8)\n",
    "predict = np.poly1d(p)\n",
    "x  = np.array(xM)\n",
    "y = predict(x)\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB, yB,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB, yB, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2 = np.poly1d(pB)\n",
    "x  = np.array(xB)\n",
    "y = predict2(x)\n",
    "plt.plot(x, y,'r')\n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.24717555  4.2701536 ] [0.47390072]\n",
      "[-4.54746011  6.00106536] [0.07725779]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2d6aa4f2f60>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM2 = np.log(average_cost_M[23:])\n",
    "yM2 = np.log(average_queue_M[23:])\n",
    "xB2 = np.log(average_cost_B[25:])\n",
    "yB2 = np.log(average_queue_B[25:])\n",
    "\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM2, yM2, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "predict_2 = np.poly1d(p)\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB2, yB2, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'r')\n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2d608a66080>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(10,6) )\n",
    "\n",
    "plt.plot(xM, yM,'go',markersize = 8)\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "plt.ylabel(\"Log Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Log Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB, yB,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'k-.', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r-.', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xB)\n",
    "y = predict2(x)\n",
    "plt.plot(x, y,'k', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xM)\n",
    "y = predict(x)\n",
    "plt.plot(x, y,'r', linewidth=2.5)\n",
    "\n",
    "plt.legend([\"\",\"\",\"\",\"\",str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2)),str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)),\n",
    "            str(round(predict2[1],2))+\"x + \" + str(round(predict2[0],2)),str(round(predict[1],2))+\"x + \" + str(round(predict[0],2))])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import curve_fit\n",
    "def model_func(x, a, b, c, k):\n",
    "    return a + b /(x - c) + k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 4.35819685e+18  5.20692726e+09  2.59760195e+07 -4.35819683e+18]\n",
      " [ 5.20692953e+09  2.60423023e+02  1.36177971e+00 -5.20692917e+09]\n",
      " [ 2.59760327e+07  1.36177970e+00  8.40513470e-03 -2.59760310e+07]\n",
      " [-4.35819683e+18 -5.20692661e+09 -2.59760169e+07  4.35819680e+18]]\n"
     ]
    }
   ],
   "source": [
    "# Fit maxweight\n",
    "x_data = average_cost_M\n",
    "y_data = average_queue_M\n",
    "initial_guess = [1, 1, 1, 1]  # Initial guess for [a, b, c, d]\n",
    "popt, pcov = curve_fit(model_func, x_data, y_data, p0=initial_guess)\n",
    "print(pcov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a_opt, b_opt, c_opt, k_opt = popt\n",
    "x_fit = np.linspace(min(x_data), max(x_data), 100)\n",
    "y_fit = model_func(x_fit, *popt)\n",
    "plt.scatter(x_data, y_data, label='Data')\n",
    "plt.plot(x_fit, y_fit, 'r-', label='Fitted Curve')\n",
    "plt.legend()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title('Nonlinear Curve Fitting')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[31.30021817 10.64304532  1.28707246]\n",
      "[[ 2.58678421e+00  5.30454796e+04 -1.69472504e+03]\n",
      " [ 5.30458994e+04  8.00533914e+12 -2.55760017e+11]\n",
      " [-1.69473845e+03 -2.55760017e+11  8.17119488e+09]]\n"
     ]
    }
   ],
   "source": [
    "def model_func(x, a, b, c):\n",
    "    y = np.exp(b - a*(x-c))\n",
    "    return y\n",
    "\n",
    "# Fit maxweight\n",
    "x_data = average_cost_M\n",
    "y_data = average_queue_M\n",
    "initial_guess = [1, 1, 1]  # Initial guess for [a, b, c, d]\n",
    "popt, pcov = curve_fit(model_func, x_data, y_data, p0=initial_guess)\n",
    "print(popt)\n",
    "print(pcov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a_opt, b_opt, c_opt = popt\n",
    "x_fit = np.linspace(min(x_data), max(x_data), 100)\n",
    "y_fit = model_func(x_fit, *popt)\n",
    "plt.scatter(x_data, y_data, label='Data')\n",
    "curve = \"exp(\" + str(round(b_opt,2)) + \"-\" + str(round(a_opt,2)) + \"(x - \" + str(round(c_opt,2)) +\") )\"\n",
    "plt.plot(x_fit, y_fit, 'r-', label=curve )\n",
    "plt.legend()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title('Nonlinear Curve Fitting')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear, High traffic, C - Cstar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"../longest_spatial_uniform_25_all_good.pkl\",'rb') as f:\n",
    "    M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "\n",
    "Q_paths_M = M_res[\"Q_paths\"]\n",
    "C_paths_M = M_res[\"C_paths\"]\n",
    "Q_paths_B = B_res[\"Q_paths\"]\n",
    "C_paths_B = B_res[\"C_paths\"]\n",
    "(average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M)\n",
    "(average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B)\n",
    "# Get the sorted indices of x\n",
    "sorted_indices = np.argsort(average_cost_B)\n",
    "\n",
    "# Sort x and reorder y accordingly\n",
    "average_cost_B = average_cost_B[sorted_indices]\n",
    "average_queue_B = average_queue_B[sorted_indices]\n",
    "\n",
    "# Get the sorted indices of x\n",
    "sorted_indices = np.argsort(average_cost_M)\n",
    "\n",
    "# Sort x and reorder y accordingly\n",
    "average_cost_M = average_cost_M[sorted_indices]\n",
    "average_queue_M = average_queue_M[sorted_indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 2.548\n",
      "[[0.         1.         2.         3.         4.         1.\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 2.         2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.         3.16227766 3.60555128\n",
      "  4.24264069 5.         4.         4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
      " [1.         0.         1.         2.         3.         1.41421356\n",
      "  1.         1.41421356 2.23606798 3.16227766 2.23606798 2.\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 3.         3.16227766\n",
      "  3.60555128 4.24264069 4.12310563 4.         4.12310563 4.47213595\n",
      "  5.        ]\n",
      " [2.         1.         0.         1.         2.         2.23606798\n",
      "  1.41421356 1.         1.41421356 2.23606798 2.82842712 2.23606798\n",
      "  2.         2.23606798 2.82842712 3.60555128 3.16227766 3.\n",
      "  3.16227766 3.60555128 4.47213595 4.12310563 4.         4.12310563\n",
      "  4.47213595]\n",
      " [3.         2.         1.         0.         1.         3.16227766\n",
      "  2.23606798 1.41421356 1.         1.41421356 3.60555128 2.82842712\n",
      "  2.23606798 2.         2.23606798 4.24264069 3.60555128 3.16227766\n",
      "  3.         3.16227766 5.         4.47213595 4.12310563 4.\n",
      "  4.12310563]\n",
      " [4.         3.         2.         1.         0.         4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 1.         4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.         5.         4.24264069 3.60555128\n",
      "  3.16227766 3.         5.65685425 5.         4.47213595 4.12310563\n",
      "  4.        ]\n",
      " [1.         1.41421356 2.23606798 3.16227766 4.12310563 0.\n",
      "  1.         2.         3.         4.         1.         1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 2.         2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.         3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
      " [1.41421356 1.         1.41421356 2.23606798 3.16227766 1.\n",
      "  0.         1.         2.         3.         1.41421356 1.\n",
      "  1.41421356 2.23606798 3.16227766 2.23606798 2.         2.23606798\n",
      "  2.82842712 3.60555128 3.16227766 3.         3.16227766 3.60555128\n",
      "  4.24264069]\n",
      " [2.23606798 1.41421356 1.         1.41421356 2.23606798 2.\n",
      "  1.         0.         1.         2.         2.23606798 1.41421356\n",
      "  1.         1.41421356 2.23606798 2.82842712 2.23606798 2.\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 3.         3.16227766\n",
      "  3.60555128]\n",
      " [3.16227766 2.23606798 1.41421356 1.         1.41421356 3.\n",
      "  2.         1.         0.         1.         3.16227766 2.23606798\n",
      "  1.41421356 1.         1.41421356 3.60555128 2.82842712 2.23606798\n",
      "  2.         2.23606798 4.24264069 3.60555128 3.16227766 3.\n",
      "  3.16227766]\n",
      " [4.12310563 3.16227766 2.23606798 1.41421356 1.         4.\n",
      "  3.         2.         1.         0.         4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 1.         4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.         5.         4.24264069 3.60555128 3.16227766\n",
      "  3.        ]\n",
      " [2.         2.23606798 2.82842712 3.60555128 4.47213595 1.\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 0.         1.\n",
      "  2.         3.         4.         1.         1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 2.         2.23606798 2.82842712 3.60555128\n",
      "  4.47213595]\n",
      " [2.23606798 2.         2.23606798 2.82842712 3.60555128 1.41421356\n",
      "  1.         1.41421356 2.23606798 3.16227766 1.         0.\n",
      "  1.         2.         3.         1.41421356 1.         1.41421356\n",
      "  2.23606798 3.16227766 2.23606798 2.         2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [2.82842712 2.23606798 2.         2.23606798 2.82842712 2.23606798\n",
      "  1.41421356 1.         1.41421356 2.23606798 2.         1.\n",
      "  0.         1.         2.         2.23606798 1.41421356 1.\n",
      "  1.41421356 2.23606798 2.82842712 2.23606798 2.         2.23606798\n",
      "  2.82842712]\n",
      " [3.60555128 2.82842712 2.23606798 2.         2.23606798 3.16227766\n",
      "  2.23606798 1.41421356 1.         1.41421356 3.         2.\n",
      "  1.         0.         1.         3.16227766 2.23606798 1.41421356\n",
      "  1.         1.41421356 3.60555128 2.82842712 2.23606798 2.\n",
      "  2.23606798]\n",
      " [4.47213595 3.60555128 2.82842712 2.23606798 2.         4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 1.         4.         3.\n",
      "  2.         1.         0.         4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 1.         4.47213595 3.60555128 2.82842712 2.23606798\n",
      "  2.        ]\n",
      " [3.         3.16227766 3.60555128 4.24264069 5.         2.\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 1.         1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 0.         1.         2.\n",
      "  3.         4.         1.         1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
      " [3.16227766 3.         3.16227766 3.60555128 4.24264069 2.23606798\n",
      "  2.         2.23606798 2.82842712 3.60555128 1.41421356 1.\n",
      "  1.41421356 2.23606798 3.16227766 1.         0.         1.\n",
      "  2.         3.         1.41421356 1.         1.41421356 2.23606798\n",
      "  3.16227766]\n",
      " [3.60555128 3.16227766 3.         3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.         2.23606798 2.82842712 2.23606798 1.41421356\n",
      "  1.         1.41421356 2.23606798 2.         1.         0.\n",
      "  1.         2.         2.23606798 1.41421356 1.         1.41421356\n",
      "  2.23606798]\n",
      " [4.24264069 3.60555128 3.16227766 3.         3.16227766 3.60555128\n",
      "  2.82842712 2.23606798 2.         2.23606798 3.16227766 2.23606798\n",
      "  1.41421356 1.         1.41421356 3.         2.         1.\n",
      "  0.         1.         3.16227766 2.23606798 1.41421356 1.\n",
      "  1.41421356]\n",
      " [5.         4.24264069 3.60555128 3.16227766 3.         4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.         4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 1.         4.         3.         2.\n",
      "  1.         0.         4.12310563 3.16227766 2.23606798 1.41421356\n",
      "  1.        ]\n",
      " [4.         4.12310563 4.47213595 5.         5.65685425 3.\n",
      "  3.16227766 3.60555128 4.24264069 5.         2.         2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 1.         1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 0.         1.         2.         3.\n",
      "  4.        ]\n",
      " [4.12310563 4.         4.12310563 4.47213595 5.         3.16227766\n",
      "  3.         3.16227766 3.60555128 4.24264069 2.23606798 2.\n",
      "  2.23606798 2.82842712 3.60555128 1.41421356 1.         1.41421356\n",
      "  2.23606798 3.16227766 1.         0.         1.         2.\n",
      "  3.        ]\n",
      " [4.47213595 4.12310563 4.         4.12310563 4.47213595 3.60555128\n",
      "  3.16227766 3.         3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.         2.23606798 2.82842712 2.23606798 1.41421356 1.\n",
      "  1.41421356 2.23606798 2.         1.         0.         1.\n",
      "  2.        ]\n",
      " [5.         4.47213595 4.12310563 4.         4.12310563 4.24264069\n",
      "  3.60555128 3.16227766 3.         3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.         2.23606798 3.16227766 2.23606798 1.41421356\n",
      "  1.         1.41421356 3.         2.         1.         0.\n",
      "  1.        ]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.         5.\n",
      "  4.24264069 3.60555128 3.16227766 3.         4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.         4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 1.         4.         3.         2.         1.\n",
      "  0.        ]]\n"
     ]
    }
   ],
   "source": [
    "[Ex,fluid_sol] = run_extremes(N, W, pmf_cust, pmf_serv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-4.8190349   5.81769843] [3.53264024]\n",
      "[-1.98643165  2.20911578] [0.17837283]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e1b9900fd0>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "\n",
    "Cstar = fluid_sol['Cost']\n",
    "xM = np.log(average_cost_M[:23] - Cstar)\n",
    "\n",
    "yM = np.log(average_queue_M[:23])\n",
    "\n",
    "\n",
    "xM = np.delete(xM, [0]) # remove outlier\n",
    "yM = np.delete(yM, [0]) \n",
    "\n",
    "xB = np.log(average_cost_B[:23] - Cstar)\n",
    "yB = np.log(average_queue_B[:23])\n",
    "\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM, yM, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM, yM,'go',markersize = 8)\n",
    "predict = np.poly1d(p)\n",
    "x  = np.array(xM)\n",
    "y = predict(x)\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB, yB,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB, yB, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2 = np.poly1d(pB)\n",
    "x  = np.array(xB)\n",
    "y = predict2(x)\n",
    "plt.plot(x, y,'r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.50088396  1.28701353] [0.16792315]\n",
      "[-2.10551365  1.916157  ] [0.00527912]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1b440948198>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "xM2 = np.log(average_cost_M[23:] - Cstar)\n",
    "yM2 = np.log(average_queue_M[23:])\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "xB2 = np.log(average_cost_B[25:] - Cstar)\n",
    "yB2 = np.log(average_queue_B[25:])\n",
    "\n",
    "\n",
    "\n",
    "p, res, _, _, _ = np.polyfit(xM2, yM2, 1, full=True)\n",
    "print(p,res)\n",
    "plt.figure( figsize=(10,6) )\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "predict_2 = np.poly1d(p)\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "pB, resB, _, _, _ = np.polyfit(xB2, yB2, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'r')\n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.79348924, -0.6469666 , -0.4345829 , -0.39465625, -0.29126398,\n",
       "       -0.19671122, -0.18799535, -0.12476127,  0.10480568,  0.37948162,\n",
       "        0.85623835,  0.8923371 ,  0.89394279])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xM2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(10,6) )\n",
    "\n",
    "plt.plot(xM, yM,'go',markersize = 8)\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB, yB,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'k-.', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r-.', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xB)\n",
    "y = predict2(x)\n",
    "plt.plot(x, y,'k', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xM)\n",
    "y = predict(x)\n",
    "plt.plot(x, y,'r', linewidth=2.5)\n",
    "\n",
    "plt.legend([\"Max Weight\",\"Max Weight\",\"Batch\",\"Batch\",str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2)),str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)),\n",
    "            str(round(predict2[1],2))+\"x + \" + str(round(predict2[0],2)),str(round(predict[1],2))+\"x + \" + str(round(predict[0],2))])\n",
    "\n",
    "plt.savefig(\"../september-report-plots/spatial-5-scale-log-log-plot.jpg\",bbox_inches='tight')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(10,6) )\n",
    "\n",
    "plt.plot(xM, yM,'go',markersize = 8)\n",
    "# plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "plt.ylabel(\"Log Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Log Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB, yB,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    " #plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "#plt.plot(x, y,'k-.', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "#plt.plot(x, y,'r-.', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xB)\n",
    "y = predict2(x)\n",
    "plt.plot(x, y,'k', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xM)\n",
    "y = predict(x)\n",
    "plt.plot(x, y,'r', linewidth=2.5)\n",
    "\n",
    "# plt.legend([\"\",\"\",\"\",\"\",str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2)),str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)),\n",
    "#             str(round(predict2[1],2))+\"x + \" + str(round(predict2[0],2)),str(round(predict[1],2))+\"x + \" + str(round(predict[0],2))])\n",
    "plt.legend([\"\",\"\", str(round(predict2[1],2))+\"x + \" + str(round(predict2[0],2)),str(round(predict[1],2))+\"x + \" + str(round(predict[0],2))])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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q1avHe++9x5gxYwDYt28PxqQASwCrx/0lKMyeneHzgZPw8DCfD6jMnp0RiDLFJZhuQV4AZFhrfw50ISJS/VT1L5+wsDCSkpJ47733qFOnDtbmAx8D7wF5FX7iUqSy9evXgsTEzkDxz17RpyMTEzvTr1+LgNUqwRXABgDvBLoIEamevH/59O7doMp++Vx99dUsW7aMxo0bu7asAV4BCs+cr/AlgTB2bFdmzerv87Pn/nfwzju9GDu2a4AqFDdjbeDvARtjIoHtQEtr7R8+9g8DhgE0atSo3YwZM/xcYXDJysoiOjo60GUEBbWFh9rCsWzZblq3DufII48o+LlLl6MJCzPk51tWrPiLc8+tD1Ds54rYtWsXDz/8MN9//71ry9HAYOBEAObPb0etWoEPX/pcOEKhHY466ihatDj8XquDBw9Sq1atSqio+qvstti8eTN///13oW1xcXFfWmvbFzvYWhvwL6AfMK88x7Zr187WdIsWLQp0CUFDbeGhtvBwt0Vi4jILyTY+/jN78GB+oWMOHsy38fGfWUi2iYnLDul19u7dZ5s3v8ACrq8ICzeU+JqBoM+FIxTa4fvvv6+U6/zzzz+Vcp1QUNlt4evvCFhjfeSZYLkFeS26/SgilaiqFybOz7fceusSMjJ6AZcCBsgF3gQ+JyXlOz1pJiIlCngAM8bUBS4CPgh0LSISOqpyYeLCAc4APbjwwrEcccQRriPmAW+RkvKVQpiI+BTwAGat3WetbWCt/bvso0VEyqcy1oYsia8nLufOfZi0tDSaN3cHuW+BiaSkLNPj/hKSfvjhBzp37kzt2rV55plnSjzOWsuDDz7Iaaedxplnnsn48eMBeOutt2jdujWtW7emS5cufPvtt1VW63PPPcdZZ51F69atueCCC/j559InXOjbty+tWnn+2/G///2PuLg4zjnnHFq3bs2nn3562DUFPICJiFSV8ixMfChPKpb0uP9ZZ53FqlWriIuLcx35K/XqTaJRo8zDeRsiQemYY45h/Pjx3HvvvaUeN23aNLZt28YPP/zAhg0bGDBgAABNmzZlyZIlrF27locffphhw4YdUh2LFy9m8ODBpR5zzjnnsGbNGtauXctVV13FqFGjSjz2gw8+KPbAxmOPPca///1vvv76a2bMmMGIESMOqVZvCmAiEtKqamHikh73b9CgAXPnzi34D/Tevbvo3r07b7zxxiG9jkiwOvbYY+nQoQMRERGlHjdp0iTGjBlDWFhYwXngLPVVv77zBHJsbCy//PILAOnp6bRu3Zrs7Gz27t1Ly5YtWbfO99JK5RUXF0fdunWLvVZRWVlZPPfcczz00EOFthtj+OeffwD4+++/OeGEEw6rHoDww76CiEgQK2th4sOZq6ukucQiIiJ4+eWXOfvss7ntttvIyclh0KBBrFu3jieffFJTAMhhu/POO/nmm28O6dzSpl5o27YtL7zwwqEX5kNGRgbvvvsuH374ITExMYwfP55TTz210DFTp07l4osvBqBDhw707duXhx56iP379zNw4MBCtwMPl/drFfXwww9zzz33FIQ1t7Fjx9KzZ09eeukl9u7dy/z58w+7DgUwEQlZ5VmYGKiyCVP/85//cPrpp3PVVVexa9cukpOT+f7773n77bc58sgjix2fmrqZPn2a+6wlP98ye3aGZi8XAL755huWLFkS6DLK5cCBA0RFRbFmzRo++OADbrrpJr744ouC/YsWLWLq1KksW7asYNuYMWPo0KEDUVFRBWPGiurUqRMHDhwgKyuLXbt20bZtWwCefvppevXq5fOc6dOns2bNGp9t980337B582aef/55tm7dWmjfO++8w+DBg7nnnntYuXIlN9xwA+vWrSvo1TsUCmAiEpJKWhty8uSeDBs2r2B7VYewuLg4Vq9eTd++ffn+++/55JNP6Ny5Mx999JHXgH0YO3Y5SUkrfY5L834viYmdNYu5FISNQ1FWD1hJXn75ZV577TUAPv3003LfhmvcuHHBYvaXX3458fHxBfvWrl3L0KFD+eyzz2jQoEHB9l27dpGVlUVubi7Z2dnUq1ev2HVXrVoFOGPApk2bxrRp00qtY/78+Tz++OMsWbKE2rVrF9u/cuVKvvzyS5o0aUJeXh47duygR48eLF68mKlTpzJnzhwAOnfuTHZ2NpmZmQW3Uw+FAlhRAwZA584wbBjUqRPoakTkEJW0NqR7YD5QKIT169eiynqXmjdvzsqVK7n++uv5+OOP+f777+nYsSMzZ84kLi6u2Jxl4AmEvuYsO+ecRuoJq+EO5zbhnj17vKZMKb+RI0cycuTICp/Xv39/Fi5cyE033cSSJUs47bTTAOfJwiuuuII333yzYJvbsGHDePTRR9myZQv33XcfEyZMqPDrevv666+55ZZbmDNnTomhafjw4QwfPhyArVu3ctlll7F48WIATj75ZBYsWMDgwYPZsGED2dnZxMTEHFZNGoTvbfFiePdduPNOaN4cxo+H/fsDXZWIHIJgW5j4yCOPZNasWdx3332A83/4PXv2ZNKkSVU6Z5lIVfn9999p3Lgxzz33HI899hiNGzcuGKh+ySWXsH37dgBGjx7N+++/z9lnn83999/PlClTAHjkkUfYuXMnI0aMoG3btrRv76zW88YbbxAeHs51113H6NGjSU9PZ+HChYdVa0JCAllZWVx99dW0bduWvn37FuwrT2/is88+y2uvvUabNm249tprmTZtGsYcZo+5r+nxg/mrSpcimjfP2lNPtRY8X8cfb+2LL1q7b1/VvW4FhcKSGpVFbeGhtvDwbotZszaVuCTQwYP5dtasTX6qyuPNN9+0tWvXLljCaMSIETY7+0DB0kglfR3K8kb6XDhCoR20FFHl01JEweKii+D77+GNN8D9hMZvv8Eddzg9Yi+9BNnZga1RRCqkX78WJY7tCgszAbmVN3DgQJYsWcJxxx0HwMSJE7n44t48/XT7Sp+zTESCkwJYUeHhcMMNniDmXnn+t9/g9tsVxESkUnTq1In09HTatWsHOE+Cde4cy513NvZ5/OHMWSYiwUcBrCTuILZhA7z+uieIbd/uCWITJiiIicgha9y4MUuXLuWaa64BnPmS2rfvCGwoduywYfO0pqRICFEAK0t4ONx4o+8gdtttCmIicljq1q3LO++8wyOPPAJAbu5+IAVYjDNEzOEemP/hh5tKDGL5+ZbU1M1VXrOIHD4FsPLyDmLTpjnBCxTEROSwWQtbtnQAbgQicYLXJwwc+B033OB5PD8lZR1XXJHKkCFzioUw93QV/fvPYuzY5f4sX0QOgQJYRYWHw6BB8MMPvoNYixbw8ssKYiJSbp45y84GRhId7cxTNH36m2za9CTXXFN4wstp09YzdOjcghDma64w9YSJBDcFsENVUhD79Ve49VYFMREpt8JzlvVk06a1nHvuuQCkpaWxfPl99OlTeOZuzRUmgWat5fbbb6dFixa0bt2ar776yudxCxcu5F//+hetWrVi0KBB5OXlAc6i1n369KFNmza0bNmSlJSUKqv1ueee46yzzqJ169ZccMEF/Pzzzz6Pe/DBBznppJOIjo4utH3p0qX861//Ijw8nJkzZ1ZKTQpgh8s7iKWkQLNmznbvIDZxIhw4ENg6RSSojR3blVmz+jNlSi+OO64RCxYsYMiQIQD88ssvzJ9/H/fcE1FswtaIiOdKnPFfpCp99tlnbNq0iU2bNjF58uSCWeS95efnM2jQIGbMmMG6des45ZRTeP311wFnaaOzzjqLb7/9lsWLF3PPPfeQk5NT4ToWL17M4MGDSz3mnHPOYc2aNaxdu5arrrqKUaNG+TyuT58+rF69utj2k08+mWnTpnHddddVuL6SKIBVlvBwGDzYdxAbOdLpIVMQE5FSeM9ZFhkZyWuvvcYLL7xAWFgY+/fv59ln7+TEE5czePBZPs9X+BJ/Sk1N5cYbb8QYQ2xsLH/99Re//fZboWN27txJ7dq1C5Yauuiii3j//fcBMMawZ88erLVkZWVxzDHHEB4eTnp6Oq1btyY7O5u9e/fSsmVL1q1bV+z1KyIuLo66desCEBsbyy+//OLzuNjYWI4//vhi25s0aULr1q0Pa/HtorQWZGWLiHCC2PXXw/Tp8Nhj8NNPniD25JNw//0wZAj4WAxURMTNGMMdd9zBGWecwTXXXMPff//NY489xuWXXw60Awr/N0RzhdUgd94J33xzSKfWOXgQSliMm7ZtoZzrTP7666+cdNJJBT83btyYX3/9tVCAadiwIbm5uaxZs4b27dszc+ZMtm3bBsCtt95K3759OeGEE9izZw/vvvsuYWFhdOjQgb59+/LQQw+xf/9+Bg4cSKtWvicoPhRTp07l4osvrrTrHSoFsKoSEQHx8TBwoBPEHn0UtmyBX37xBLEHHoCbblIQE5FS9erVi1WrVtGnTx82bdrEhx9+CKQB8UD9guOGDZunHrCa4ptvYMmSQzq1sn7xO6vsFFZ0fURjDDNmzOCuu+7iwIED9OzZk/Bwp4K5c+fStm1bFi5cSEZGBhdddBHdunXjyCOPZMyYMXTo0IGoqCjGjx/v8/U7derEgQMHyMrKYteuXQVrOj799NP06tXL5znTp09nzZo1LDnEtqtMCmBVzTuIvfmm0yPmDmIjRsATTyiIiUiZTj/9dFauTKN16wvZvv1r4DfgRWAQ0BSgYCyYQlgNUI4FpEuSd/Ag4aX1gJXg5Zdf5rXXXgPg008/pXHjxgW9WeCMVTzhhBOKnde5c2e++OILAObNm8ePP/4IQEpKCqNHj8YYQ4sWLWjatCk//PADHTt2ZNeuXWRlZZGbm0t2djb16tUrdt1Vq1YBzhiwadOmMW3atFLf9/z583n88cdZsmQJtYPg960CmL9ERDgh64YbfAcxd49YfLyCmIgUk59vSUhYzfbt1wD1gGXAXiIiXqNjx5EsX34iUHoIS03dTJ8+zX2Gs/x8y+zZGQFZG1MOQTlvE/qyf88ejjjiiAqfN3LkSEaOHFnwc9++fZkwYQIDBgxg1apVHHXUUT7HT+3YsYNjjz2WAwcO8PTTT/Pggw8CzsD2BQsW0K1bN/744w82btxIM9f46WHDhvHoo4+yZcsW7rvvPiZMmHCI79bx9ddfc8sttzBnzhyOPfbYw7pWZdEgfH9zB7GNG2HKFGjSxNm+bRsMH+4sAv7KKxqsLyKFeOYKqwX0o2vXO4iIiCA3N5fly1/grLOWAwcBJ4TNnp1R6PyxY5fTv/+sQvOHuWkSVzkUl1xyCc2aNaNFixbcfPPNTJw4sdC+7du3A5CcnMyZZ55J69at6dOnD+effz4ADz/8MCtWrODss8/mggsu4Omnn6Zhw4a88cYbhIeHc9111zF69GjS09NZuHDhYdWakJBAVlYWV199NW3btqVv374F+9p69fqNGjWKxo0bs2/fPho3bszYsWMBSE9Pp3Hjxvz3v//llltuoWXLlodVD+Dcw61OX+3atbMhJSfH2ilTrG3SxFpnQmzn66STrJ00ydrs7GKnLFq0yP91Bim1hYfawiNU2yIxcZmFZBsf/5k9eDDfLl261DZs2NDiTJ1vTzyxnYVHbGLisoJzFi1aZGfN2mQhueDLfb611h48mG/j4z8rtH/WrE2BeotVJhQ+E99//32lXOeff/6plOuEgspuC19/R8Aa6yPPqAcs0CIinCciN26E117z3SP26qtwCHOjiEho8Z4rLCzM0K1bN9LT0zn77LMB+PXXLznxxGlcd11MofP69GlebP4wTeIqElgKYMEiMhKGDvUEsVNOcbZv2wb/+Y+CmIgAhecKA2d+ohUrVtCvXz8Afv31Jzp16sTnn39ecExYmGHKlF6axFUkiCiABRt3EPvxx8JB7H//Kwhix8+erSAmIgWio6P54IMPCgY3//XXX1x88cWMHz++YKoAXyHMm8KXiH8pgAUr7yA2eXKhIHb6c885PWKTJyuIiQgAYWFhPPbYY7z99ttERUVx8OBB7rjjDp599tmC5V3CwgyTJ/f0eb4mca0e3IFagk9F/24UwIJdZCTcfLMniJ18srP9f/+DW25REBORQq699lqWLl1aMB/TJ598wkUXXcSff/5Jfr5l2LB5Ps8bNmxesacjJbhERUWxc+dOhbAgZK1l586dREVFlfsczQNWXbiD2KBBbLz/fk6fOdMJYe4g9sQT8OCDzsLgkZGBrlZEAqhDhw6kp6dz+eWXs3r1apYuXUrHjh1p02YUqal7fZ6jSVyDX+PGjfnll1/4888/D+s62dnZFQoKoawy2yIqKorGjRuX+3gFsOomMpLf+vTh9CefhGnT4PHHnRD2888wbJjzs4KYSI13wgknsHjxYvr27cv8+fPZunUrW7feBQwAWhEf34rJk3sybNi8gvClEBbcIiIiaNq06WFfZ/HixZxzzjmVUFH1F8i20C1Il6ycLBIXJRKTHENYUhgxyTEkLkokKycr0KX5FhnpBK5Nm5yJW90LorqD2OmnOxO95uYGtk4RCZg6derwwAMPcMMN9wIGOAC8Qbt263nttZ6Eh4f5fDqy6CSuRaWmbi7xdmV+viU1dXPlvQmREKUAhhO+YqfEMm7FODL3ZWKxZO7LZNyKccROiQ3eEAZOELvlluJBbOtW55blaacpiInUYMYY3ngjmQEDngRqA5Yvv5zGjTfewP79+4s9HZmY2LnU5Yg0o75I5VAAA5KXJ5OxO4PsvOxC27PzssnYnUHy8uQAVVYBtWt7gtikSQpiIlLIO+/cx4svflBwC+vtt9+me/fubN++vSCEzZrVn7Fju5Z4jdTUzSQlrQQ8k7m6Q5g7fLlvYyYlrVRPmEgpFMCAiWsmFgtfbtl52UxaM8nPFR2G2rWd+cJKC2JTpyqIidRAt99+CatXr6Z79+6As76de8B+WJgpcyFuzagvUnkUwICd+3aWvn9/6fuDUtEg5n4yY+tWZ34xBTGRGqlhw4bMmzePW265BYDt27dz3nnn8c4775R5rmbUF6k8CmBAg7oNSt9fp/T9Qc0dxDZvhokTiwex00+H//s/BTGRGiQyMpJJkyYxYcIEatWqRXZ2Ntdddx0PPvgg+fn5pZ6rGfVFKocCGDCi/Qiiwn3PAxIVHsXw9sP9XFEVqF3bWdy7aBDbssVZDFxBTKRGMcYwcuRI5s6dS/369QF44oknuOKKK9izZ0+p52pGfZHDpwAGJHRNoHn95sVCWFR4FM3rNyeha0KAKqsC3kHs5ZfhxBOd7e4gdsYZkJKiICZSQ1xwwQWsWrWKM844A4DU1FS6dOnCli1bSjxHM+qLHD4FMCA6Mpq0oWmM6jKKmLoxhJkwYurGMKrLKNKGphEdGR3oEitf7dowYgRkZBQOYj/9BDfdpCAmUoOceuqppKWl0bt3bwDWrVtHx44dWbp0abFjiz7tWFTRpyNFxDcFMJfoyGiS4pLYkbCDg2MOsiNhB0lxSaEZvrwpiIkIcNRRR/Hxxx9zzz33AJCZmckFF1zAa6+9VnCMr/AVH9+K3Ny7fT4dqRAmUjIFMHG4g9jmzTBhQvEgduaZztJHeXkBLVNEqk6tWrV45plnmDZtGpGRkeTl5TFs2DBuv/128vLymD07w+fTjoc6o75ITaYAJoVFRcHIkZ4gdsIJzvaMDIiPd3rEFMREQtqgQYNYtGgRxx57LAAvvfQSF198Meed14DExM5A8acdKzqjvkhNpwAmvrmDWEYGvPSS7yD2+usKYiIhqkuXLqSnp9O2bVsA5s+fT6dOnRgwoAGzZvX3OdVEeWfUFxEFsJBRZYuJR0XBrbf6DmKDByuIiYSwk08+mWXLlnHllVcCsGnTJmJjY6lde3OJU02UZ0Z9EVEACwl+WUzcO4iNHw/HH+9sVxATCWn16tXjvffeIzExEYC///6bSy+9lOeffx5rNche5FApgIUAvy4mHhUFt93mDM73FcTOPBPeeENBTCSEhIWFMXbsWN577z3q1KlDfn4+d999N0OGDOHAgQOBLk+kWlIACwEBWUy8pCC2eTMMGqQgJhKCrr76apYtW0Zj10oaKSkpnH/++fzxxx8Brkyk+lEACwEBXUzcHcQyMuDFF4sHsbPOgjffVBATCRH/+te/SE9Pp3Nn52nIFStW0KFDB7755pvAFiZSzSiAhYCgWEy8Th24/XZPEDvuOGf7pk1w440KYiIh5LjjjmPRokUMGjQIgG3bttG1a1c++OCDAFcmUn0ogIWAoFpM3B3EfvoJXniheBBr2RKmT1cQE6nmateuTUpKCsnJyRhj2LdvH1deeSWPPPKIBueLlIMCWAgIysXE69SBO+4oHsR+/BFuuEFBTCQEGGO49957+fjjjznyyCMBSExM5JprrmHfvn0Brk4kuCmAhYCgXky8vEHs4MHA1Sgih+WSSy5h5cqVNG/eHID//ve/nHvuuWzbti3AlYkELwWwEBH0i4l7B7Hnn4dGjZzt7iB21lnw1lsKYiLV1FlnncWqVas4//zzAfj666/p0KEDaWlpAa5MJDgpgIl/1akDd97pO4gNHOj0iCmIiVRLDRo0YM6cOYwcORKAP/74g+7du/PGG28EuDKR4KMAJoFRt64niD33nCeIbdzoCWJvv60gJlLNREREMGHCBF555RXCw8PJyclh0KBBjBo1ioP69yxSQAFMAqtuXbjrroIglt/oWGf7xo1w/fVsOr42Mx+6gqz9fwe2ThGpkFtuuYXPP/+cY445BoDk5GT69u3LP//8E+DKRIKDApgEh7p1yRp5Mx1HN+C+i8P5o56z+dQ/D3LV4x+yo+mxZL+Zoh4xkWqkR48epKen07JlSwA+/fRTYmNj2bx5c4ArEwk8BTAJGsnLk1m/dwvjOuXR9A64uycFQazZHzlE3XgTtGoF77yjICZSTTRr1owVK1Zw2WWXAbBhwwY6derEwoULA1yZSGApgEnQ8F7Tcn8kPN+FYkGMH36A666Ds8+GGTMUxESqgSOPPJJZs2Zx3333AbBr1y569uzJxIkTA1yZSOAEPIAZY442xsw0xvxgjNlgjOkc6JokMHytaekOYs3ugHt7GjjWNUZswwa49lo6DBmiICZSDdSqVYunnnqKN998k9q1a3Pw4EFGjhzJ8OHDyc3NDXR5In4X8AAGvAjMsdaeAbQBNgS4HgmQ0ta03BcJb1zY0Bms/8wzEBMDQL2ff4Zrr4XWreHddxXERILcwIEDWbJkCce5JmV+5ZVX6NmzJzt3Fv8fMJFQFtAAZow5EjgPmApgrc2x1v4VyJokcMq1pmW9enDPPbBlCyQnk3P00c4B338PAwZ4glh+vv8KF5EK6dSpE+np6bRr1w6AxYsX07FjR9avXx/gykT8J9A9YM2AP4EUY8zXxpgpxph6ZZ0koalCa1rWqwf33kva229DcnJBj1hBEDv7bHjvPQUxkSDVuHFjli5dyjXXXAPATz/9ROfOnfn4448DXJmIf5hArlpvjGkPpAFdrbWrjDEvAv9Yax8uctwwYBhAo0aN2s2YMcP/xQaRrKwsoqODZImhSrb/4H5mbJvBR9s/4u/cvzkq4ij6ntCXAScNoE6tOsWOd7dF2P79nJiaykkzZhD5t2fOsL1NmrD1xhv5s3t3CAv0/29UrVD+XFSU2sIj2NvCWsv06dP5v//7P8BZ4Pvmm29mwIABGGMq7XWCvR38SW3h4Y+2iIuL+9Ja277YDmttwL6A44CtXj93Az4p7Zx27drZmm7RokWBLiFoeLfFngN77GOfjLZjL6lrd9TFWry+Wra09r33rD14MHDFVjF9LjzUFh7VpS0++OADW69ePQtYwN5www12//79lXb96tIO/qC28PBHWwBrrI88E9AuAWvt78A2Y8zprk0XAN8HsCSpprJysoidEstjX7/A2I77aHoHjLoQ/qzrOmD9evj3v50xYv/9r25NigSZyy+/nBUrVnDKKacA8Oabb9KjRw9+++23AFcmUjWC4Z7MbcBbxpi1QFvgicCWI9VR8vJkMnZnFMwjtrc2JJ/rzCP2YK9w9h7lSmLuINamDcycqSAmEkRat27N6tWrOffccwFYtWoVHTp04MsvvwxwZSKVL+ABzFr7jbW2vbW2tbW2v7V2d6BrkurHexJXb3trwxOd82h1b114+mlo2NDZsW4dXH21gphIkDn22GNZsGABQ4YMAeDXX3+lW7duvPvuuz6PT03dTH6+77HM+fmW1FQteyTBKeABTKQy+JrE1dv/8nfBqFHO9BVPPQUNXHOOKYiJBJ3IyEhee+01XnjhBcLCwti/fz8DBgxgzJgx5Hv9Gx07djn9+89i6NC5xUJYfr5l6NC59O8/i7Fjl/v7LYiUSQFMQkJpk7gCNKjj2h8dDffdB1u3+g5ibdvC++8riIkEmDGGO+64g08//ZSjjjoKgEcffZSrrrqKrKwsUlM3k5S0EoCUlHWFQpg7fKWkrAMgKWkly5bp5ooEFwUwCQnlmsTVmzuIbdkCTz7pCWLffQdXXaUgJhIkevXqxapVqzjttNMA+PDDD+natSutW4cTH9+q4Dh3CMvLyy8UvgDi41vRpcvR/i5dpFQKYBISKjSJq7cjjoDRoz1B7JhjnO3uIHbOOfDBBwpiIgF0+umnk5aWRs+ePQFYu3YtnTp1ZPDgesVCWETEc8XC15QpvQgLq7w5xUQqgwKYhIToyGjShqYxqssoYurGEGbCiKkbw6guo0gbmkZ0ZBkT7bmD2Nat8MQTniC2di1ceaWCmEiA1a9fn08++YQ777wTgD///JMLL7yAzp1/KRTCvBUNXxqUL8FEAUxCRnRkNElxSexI2MHBMQfZkbCDpLikssOXtyOOgPvvLzmI/etf8OGHlRbEsnKySFyUSExyDGFJYcQkx5C4KJGsnKxKub5IKAkPD+f5559nypQpREREkJuby7BhN3PEEXOAg8WOnzy5Z6HwpUH5EkwUwER8KSmIffstXHFFpQQx9+Sx41aMI3NfJhZL5r5Mxq0YR+yUWIUwkRIMGTKEBQsW0NA1rcz48S8C/wfsL3TczTc7A/Pz8y3JyVsLDcpXT5gEmgKYSGncQWzLFnj88UoNYkUnj3XLzssmY3cGycuTK+MdiISkbt26sWrVaurXb+La8iPwEvBnwTHTpq3nppvmMGTIHObM8UxVEx/fij59mvuzXJFiFMBEyuPII+GBBzxBrH59Z7s7iLVrB7NmOStPllNJk8eCE8ImrZlUCYWLhKb8fMtjj21k9+6hQEvX1j+JiHgZ2Fhw3Ouvr2fatPUFP2tQvgQLBTCRinAHsa1b4bHHPEHsm2/g8sudHrFyBrGyJo/dub/0/SI12ezZGa5birWBG2nT5loAcnP3Ysz/AV/grOvtUVbPlwbpiz8pgIkciiOPhAcfLD2IpaaWGsTKPXmsiBTTr18LEhM7AxAf35qvvnqLd955h6ioKKzNBz4CZgJ5Bec0bhzNFVekauZ8CQoKYCKHo7Qg1r+/c2uyhCBW4cljRaSQsWO7MmtW/4JbigMGDGDJkqXULfifm9XAZMB5oOXRR9OA8s2cr54wqWoKYCKVwR3EtmyBRx+Fo492tn/9tSeIffRRoSB2yJPHikiBfv1aFJpq4pVXdrJv33DgJNcRW4DxwPZC55U1c74G6UtVUwATqUxHHQUPPeT0iBUNYv36FQpi3pPHNqzjPE5vMGTnZfN71u8kL0/WVBQi5VS4F+soYDjNmsW59u4GXgbWFTpHM+dLICmAiVQF7yD2yCMlBrHoiHokdE2gUXQjosKjsK5Bwzv379R8YCIV4BmU74iPP4cff5zPU089hTEGyAFeBxZQdHC+5xyFL/EfBTCRqnTUUfDwwyUHsfbtSU0eSsauzZoPTOQwFB6U7wSpWrXCuO+++0hNTaVOnTquI+fQsuU8ILfYNdwz56embi42SN9NT0pKZVEAE/GHkoLYV19x/UPvsmziAS7bSLH/Mdd8YCLlV3RQvlufPn14+eWXadq0KQDr188HJgJ/Fzp/2LB5JCYup3//WXpSUqqcApiIP7mD2JYtkJTk/Ay0+w1mvwNrJlMsiGk+MJHy8x6U761p06akpa3iuOPOdm35BWdw/v8KjklJWccjj6ws+F5PSkpVUgATCYSjj4YxY2DrVp66qC5/1XY2u4NY+mS41BXENB+YyOHLz7eMHv0lv/9+HRDr2voPtWtP5rzzdvg8R09KSlVSABMJpKOPZv/993LGvbVJ7EFBEGv/G3z8Dqx5zfB87gUVWuLocGTlZJG4KJGY5BjCksKISY4hcVGiHgSQam/Fir9cASocuJLY2JHUqlWLAwcOsHRpMmefnQ4UX9NVT0pKVVEAEwmwhK4JNDyhBeMujKLJnRQKYu22W65/cAZ07AiffFKlQSwrJ4vYKbGMWzGOzH2ZWCyZ+zL1NKaEhHPPrV9okP7y5S8xd+5c6rsmT/7uu/c46aQPgWzGjIklPr6Vz+sofEllUQATCTDv+cAiG8TwWFwY7R9owKIbz8O6xoixZg1cdlmVBrHk5clk7M7Q05gSsooO0r/gggtYvXo1Z5xxBgDbtqVx8slvMnjwiUye3NPnNV555SKf4UtPR0pFKYCJBIHoyGiS4pLYkbCDg2MOsnlMJnGvL8Fs3QqJic5M+1ClQWzimonFwpebnsaUUFF0kH6LFi1IS0vj4osvBuB///uRDh060LfvMz7Pb9Uqhby8wrcq9XSkHAoFMJFgdvTRMHasM32FryDWqRN8+mmlBLGd+0p/2lJPY0qoOuqoo5g9ezb33nsvADt37uSzz+4H0oodu2nTX5x11v8VhDA9HSmHSgFMpDqoX98TxMaM8QSx9HS49FLo1Ilj0tIOK4g1qFv605Z6GlNCWa1atXj66XGce+7dQC2cAfnvc+aZS9m79zZOPfXogmPdISwn56CejpRDpgAmUp3Ur+/MH+YjiLW+/36IjYXPPjukIDai/YhiC4O7RYVHMbz98MMoXCT4zZ6dwbJlxwP/AaIB2LBhNn37XsqyZf2LhbDatZ8vFL4GD27pc4C+xoeJLwpgItWRO4ht2eJM7HrEEc721avhkksOKYgldE2gef3mxUJYVHgUzes3J6FrQmW+A5Gg41nOqAlXXz2Rc845B4AFCxbQtWtnPvigS6EQVh4aHyYlUQATqc6OOcZZ2mjrVrbecEPxINa5M8yZU64g5v00ZsM6DQEwGLLzsvk963eSlydrKgoJee4nJWfMGMgXX3zBVVddBcDmzZvp2rUzzzxzXInnTpu2XrPnS7kpgImEgmOOYetNNzm3Jh96yBPEVq2Ciy8udxCLjowmoWsCjaIbERUehXWtibRz/07NByY1hvtJyXr16vHuu+8yduxYAP755x/69+8HLKHYwq0umj1fyksBTCSUHHMMPProYQUxzQcm4hEWFkZiYiLvvvsetWrVxtp84GPgPSDP5zllzZ6vMWECCmAioamsINalC8yd6zOIaT4wkcLy8y1z5hzBwYPDgaNdW9fQufNsBgw4sczzi4YvjQkTUAATCW3uILZlCzz4IEQ7T3aRlga9e/sMYpoPTKSw2bMzXL1ZJwK3ERNzJgArV65g+fL76Nu3Tqnnu2fP15gw8aYAJlITNGgAjz3m9Ij5CmJdu8K8eWCt5gMTKcLzdCTEx3fh55+/YtCgQQBs27aN+fNH0aPH7hLPb9UqRXOGSTEKYCI1iXcQe+ABTxBbuRJ69YKuXXnW9iKqVm2fp1fFfGBZOVkkLkokJjkGk2So+3hd6j1ej7CkMGKSY0hclKiB/xJw3utI1qkTRUpKCs888wxhYWHs27ePxYufAD7H1+B8X3OGaVFvUQATqYkaNIDHH/cZxG687y1WpIRxydaIQr9LqmI+sKycLGKnxDJuxTgy92UCsD9vP/vy9mGxZO7L1NOXEjS815E0xnDPPffw0UeziYio6zpiHjCdgQNbcODAXSXOGabwJVDBAGaMOdsYM8QY86Ax5lFjzF3GmEuNMfWrqkARqULuILZlC9x/f0EQO+en/XwyLZdV08Lp+ZMhpk5DRnUZRdrQNKIjoyvt5Ut64tKbnr6UYJaXdxq5uSMA9635taxf/wh//LGddevifZ4zeXJPhS8pO4AZY5oZY5KNMduBb4BXgDuBeOBRYDbwpzFmgTHmWmOMetVEqpuGDeGJJ4oFsY4/5zH3DcuO1NNIyjuX6Ih6lfqypT1x6U1PX0qwcsaH9Qdu5/jj2wLw9ddf06FDB664YrzPc4YNm1cwWavUXKWGJWPMFGA90BZ4BDgHiLLWxlhrG1tro4FjgT7Ad8A4YIMx5twqrVpEqoZ3EBs9Guq5AteKFdCzJ3TrBvPnH9ai397KeuKy0LF6+lKClDM+7Dq2bFnFrbfeCsAff/zBJ58kAGuKHe+erNU7hGlusJqnrN6qbOAMa+1F1tpXrLVrrbUHvQ+w1mZaaz+z1t4JnAKMwXlWV0Sqq4YN4cknnTFi3kFs+XK46KJKC2JlPXFZ6Fg9fSlBrF+/FtSuHcmLL46nc+fbcH69HgTepVWrNB58sEOh471DmOYGq5lKDWDW2luttT+X92LW2nxr7bvW2ncPvzQRCTh3ENuyBe67r3gQO+88WLDgkIPYiPYjii3+7UtVPH0pUhVmz85g5cqTgWGAMzh/3br3efzx/wD7Cx2bkrKO1NTNmhushtJ4LREpW0wMPPVU8SC2bBlceOEhB7GErgk0r9+81BBWFU9filQVz5xhzbnqqgm0bNnStecHYAKQWXDsww/Hek3y6tDcYDVHuQOYMWaTMea/xpiHjDF9jTGnVGVhIhKEKjmIRUdGkzY0jVFdRhFTNwaDoW54XepG1MVgiKkbUyVPX4pUJfecYe++O5iVK1fSp08f154dwHjA6eF69NE0zQ1Wg5UYwIxjjDHmONemqUAXnMH4s4CfjDG7jTFLjTEvGWOGGmM6GmNKX5NBRKo/7yA2ahTUdc2D5A5i3bvDwoXlCmLRkdEkxSWxI2EH+Yn57H1wL3sf2Et+Yj47EnaQFJek8CXVjnvOsCOOOIIPP/yQ0aNHu/bsB14DVhQ6XuGr5imtBywMSAROcP0cA/wBdAWOBzoCTwOnAwOAZCAN2GOM+aGqChaRIBITA08/7QzW9w5iX3wBF1xQoSAmEqpq1arFk08+yfTp06lduzaQD3wIvI8zUF9zg9VEZd2C9P40xAMPWmtXWmv/sNZ+aa19CmgJ/A9nKopmwNXAO1VSrYgEp7KCWI8esGiRgpjUaNdeex0XXfQ0cKRrSxpOb9hezQ1WA1VkEL7F/UiH90ZrM3F6wsZZa7daaz+01iZVVoEiUo24g9iWLZCQ4AliS5fC+ecriEmN5Z5q4uOPc4HbgcauPRnAeFJS5hebG0xCW2kBzAI/AwdcP88EHjbGHOXj2CygdSXXJiLV1bHHwrhxZQcxkRrAHb48A+6P4oYbJnDNNde4ft4FTCAl5T2GDp3Lhx9uKjGIacLW0FFiAHPN6dXUWrvetSkBZ/Tgj8aYh40xXYwxJxtjugOPA5v8UK+IVCflCWKLFweyQpEq52uqiWnT+vLOO+/w6KOPurYeAKaRkvISV1wxy2dvmCZsDS3lvgVprf0H6Aa8AIwAlgFbgEU4A/T/UwX1iUgo8A5i994LdVwPSy9ZAnFxCmIS0jxzgxV+2tEYw0MPPcTMme8THh6Fc+PpU2AGKSlfFwphRXvRNGFr9VehiVittXnW2idxnoxsA1wKdAKaWWtXVUF9IhJKjj0WkpMVxKTGcc8N5muqiSuvvIL09DRiYtyr+H0FTCIlZQVDh84lLy+/yC1MTdgaCg5pJnzr+M5aO8dam26tzanswkQkhDVq5Ali99xTPIjFxTnfi4QQ99xgvrRt24b167+mW7duri3bcAbnf0ZExHOasDUElRrAjDE3GGNqVeSCxpgWxphuZR8pIjVeo0bwzDPFg9jixU5vmIKY1CAxMTHMnz+fIUOGuLb8DUwEvik4pmj40qD86qusHrB7gAxjzKPGmDYlHWSMaWCMud4YMxv4GmeiVhGR8ikriJ1/vjNwXyTERUZG8tprr/Hccy/gTMWZB7wFzAHyC03YqkH51VupAcxa2xa4D4gDvjbG/GOMWWWM+cQY84ExZqExZgvOAlcv4kxocoa19r2qLlxEQpA7iP30E9x9tyeILVrkzKqvICY1gLXw3XenA0MA90L1C4A3GTx4Fvn5VoPyQ0CZY8Cste9aa88FTsOZiuIbnEheD2dpoteB3sDx1to7rbW/Vl25IlIjHHccPPusgpjUOIWD1ek4k7bGuPau4623buXf/36dIUPmaFB+NRde3gOttZtxL+EuIuIP7iCWkOAM2p84EbKznSC2aJETxMaOhW4adirVX/EJW2Hw4B5kZ7djxoyHgR+B33j//VuBQUBTQIPyq6tyPwVpjNlgjHnHGDPaGNPbGHNi2WeJiFQCdxDbsgXuuguiXLdlFi6E885z1pv84ovA1ihymHxN2Dp1am/eeutqbrzxWZypOAH2Aq8Cq4uFr9TUzZpFv5qoyDQUb+LM+fUEzkxx/zPGZBpjFhhjnjXG9DfGRFZJlSIi4ASx554rOYhdeCEsWxbYGkUOUUkTtoaFGaZOvQToC1wN1AIOAv/liCPmkJ9/EICxY5fTv3/Zs+hPm6aRQsGgIgEsH/gHOA84CeiMswj36UA8MAUnlF1Z2UWKiBTiDmI//QR33ukJYgsWQLdutLnnHgUxqZZ8Tdian28ZNmye64iOwDCcYdgwfvyLXHrpZbz11lckJa0EICVlXamz6L/++m/qCQsCFQlgdwMPWGuXWWt/tdauttYmAy1xxobF4/SOvWWMuaC8FzXGbDXGfGeM+cYYs6ZC1YtIzXb88fD888WCWP2vvnLGhV10ESzX4/lSvXhP2OprXBg0A+7APePTvHlzefTR67jiiqMLjnCHMF+z6Pfu3UAD9oNARQJYOHBU0Y3W2r9xgtfD1trxwFTgoQrWEWetbWutbV/B80RECgexO+4gPyLC2T5/Ppx7roKYVEu+wld8fCtyc+8mPr4bMBKnDwQ2btzIwoUJ9Ox5oODYlJR1PmfRT0hoogH7QaAiAexDYIwxpoGPfXm4PwXO+DAFKRHxv+OPhxdeIO3tt+GOO6B2bWe7gphUQ74G5U+Z0ovw8DCmTOlFfHw74EbAuen0119/MX/+GDp23IyzsHdheloyuFQkgN0L7MOZGX+MMeZfxpjGxpgeOD1gP7iOy6ngdS0wzxjzpTFmWAXOExHxKadhQ3jhBadH7Pbbiwexnj1hxYoqe/2snCwSFyUSkxxDWFIYMckxJC5KJCsnq8peU0JPSYPyAcLCjCuEtQZ6c+WVY4mKiiI/P5/Vq18FZuL0jXh4z6IvgWes9f24qs+Dnacc78fp92yIE54MzqqhV1lr040x9wPXW2tblfOaJ1hrtxtjjgU+B26z1i4tcswwnFGHNGrUqN2MGTPKXXMoysrKIjo6OtBlBAW1hYfawqNoW0RmZnLyO+9wwuzZhOXmFmzf1b49WwcN4p9W5frPVbnsP7ifEV+NYHv2dnLyczw1hEVyQtQJTPzXROrUqlNpr1cWfS4c1bkdli3bTZcuR/sMT/n5lhUr/uLcc+uzceNGHnroITIzM117m+L0kDnvu3fvBiQkNGHfvr3Vti0qmz8+F3FxcV/6GmJVoQBWcJIxBmiNMwIwE/jWWpvr2tcdqGut/ewQrjsWyLLWPlPSMe3bt7dr1tTssfqLFy+mR48egS4jKKgtPNQWHiW2xa+/wtNPw+TJcMAzVoaePZ0JXTt3PuzXTlyUyLgV48jOyy62Lyo8ilFdRpEUl3TYr1Ne+lw4akI75OdbrrvuHd59dzROvwhAfWAwcALg9KQNHFib88+PC0yRQcYfnwtjjM8AVpFbhRhjjjLGDMB5IrIVsMFau8YdvgCstUvKG76MMfWMMUe4vwd6AutKP0tE5BCdeCKMHw8ZGXDbbZ5bk/PmQZcu0KsXrFx5WC8xcc1En+ELIDsvm0lrJh3W9UV8cQ/Yf/fd7cBw4F+uPbsJD5+E+1drSso6kpO3ljhZq/hPRWbCbw1sxFmW/SGciVl/MsZ8fBiz4jcClhljvgVWA59Ya+cc4rVERMqnrCDWu/chB7Gd+3aWvn9/6ftFDkXhAfsRDB78GE8++STGGPLysnGWbV4AWObM2cns2RmBK1aAivWAvQR8DcRYa+vj3FTui7NKaJox5viKvri19idrbRvXV0tr7eMVvYaIyCHzDmK33gqRrsU85s495CDWoK6vB8U9jok6RgP0pdIVHbA/dWpvRo8eTWpqqtcYpznA21x/fQP69WsRsFrFUZEA9i/gWWvtLgBr7T5r7SdAF5yesaeqoD4Rkap34onw0kulB7G0tHJdakT7EUSFR/ncV7tWbYwxjFsxjsx9mVgsmfsyGbdiHLFTYhXC5LD4mkW/T58+pKWl0axZM9dR37BmzdP8+quWIwq0igSwXUCx/7Wz1h4EXgAurqSaREQCo3FjTxAbObJwEOvcGS6+uMwgltA1geb1mxcLYVHhURxR+wj25OwpNkYsOy+bjN0ZJC9PrtS3IzWP9yz6bi1btmTVqlUFg803btxIhw4dWL16dbHztWC3/1QkgL2LMxFrfR/7DM5M+SIi1V/jxjBhQvEgNmeOJ4itWuXz1OjIaNKGpjGqyyhi6sYQZsKIqRvDqC6jsNZqgL4ERMOGDZk3bx7t2vUH4LfffuO8887jrbfeKjjGe8HusWM1YXFVq0gASwT2AOuMMfcbYzoYY05yTTvxKPBFlVQoIhIo7iC2eTOMGFE4iMXGwiWX+Axi0ZHRJMUlsSNhBwfHHGRHwg6S4pLYtX9XqS+nAfpSlT799Ge+/LIrcDkQxoEDBxg4cCD3338/eXkHCy17lJS0Uj1hVazcAcxaux/ogfMU5CggDdgKLMKZbvfWyi9PRCQInHQSvPxy8SD22WeeIObjdk5RZQ3Qb1Cn9P0ih6NPn+bEx7fCGbo9FHAmBH7qqado1qwrKSmeOTbj41tpwe4qVmoAM8bU8v7ZWpttrR0FHAvEApcCZ1tr21trt/m6hohIyPAOYsOHg3vR788+g06d4NJLSw1ipQ3QjwqPYnj74VVRtQjgWb6od+8GwKnA7Ti/zmHbtlXABGCn1oz0k7J6wPYZY74yxqQYY+4wxvQwxtS31uZaa9OttXOstev9UqmISLA46SSYOLF4EPv001KDWGkD9JvXb05C1wR/VC81WFiYISGhiasnrCHOzaszXHv/oHbtidxwQ5TClx+UFcAG4Uwc0gjntuNCINMY87Mx5iNjzKPGmCuNMZpQRERqnpNP9gSx//ynzCBW2gD9tKFpREdqfT6pemFhhsmTe7p+qgPEA90BOHDgH3r2vIjJkycHqrwao9QAZq2dYa19wFp7ibX2RJy+yl7AeOAvoB/wDvCjMWZPVRcrIhKUTj4ZJk0qOYhddhmkpwMlD9BX+BJ/yc+3DBs2z2tLGHAZcA1hYeHk5eVxyy23cNttt5HrtXi9VK4KrQVprc201s631j5rrb3RWtsaqAe0Q4PwRaSmcwexTZvglls8QeyTT6Bjx0JBTCQQ8vMtyclbvZYt8tae/PxbqFPHmW1qwoQJXHzxxezaVfrTu3JoKhTAfHGNB/vaWvt6ZRQkIlLtnXIKvPJKyUGsTx9Ys6b0a4hUMvc8X3PmeKY7iY9vRW7u3a4xYQBN2L9/BMcc4zwBuWDBAjp16sSGDRsCUHFoO+wAJiIiJSgpiH38MXTooCAmflV4wW4KnnYMDw9jypReXiHsaHbtuokuXZwFbjZv3kxsbCyfffZZAKoOXQpgIiJVzTuIDRtWPIj17QtffhnYGiXkFV2w23uqCfcUFe4QlpjYnWXLPiEpKQmAf/75h8suu4xnn30Wa21g3kCIUQATEfGXU06BV1/1BLFw1wpus2dD+/YKYlLlxo7tyqOPNvc5z5c7hM2a1Z+xY7tijGHMmDHMnDmTunXrkp+fz7333stNN93EgQMHAvQOQocCmIiIvymISQCde279Euf5Cgsz9OtXeGapK6+8kuXLl3PSSScBMG3aNOLi4vj999+rvNZQpgAmIhIoTZp4gtjNNxcPYv36wVdfBbREEYC2bduSnp5O587OLcyVK1fSsWNHvv766wBXVn0pgImIBFqTJjB5cvEg9tFH0K6dgpgEhUaNGrFo0SIGDx4MwLZt2zj33HOZOXNmoePy860W8i4HBTARkWDhDmI//ghDhxYPYv37Qzl7HLJyskhclEj/Ff0JSwojJjmGxEWJZOVkVVn5Evpq167NyScPAS7DmDD27dvH1VdfzdixY8nPzy+Y6qJ//1mMHbs80OUGNQUwEZFg07QpvPZa8SCWmgr/+leZQSwrJ4vYKbGMWzGOv3P/xmLJ3JfJuBXjiJ0SqxAmhyw1dTOPPJIGdMfaeCIi6gKQlJTEv/99DYMGpRZMdZGUtFI9YaVQABMRCVaHGMSSlyeTsTuD7LzsQtuz87LJ2J1B8vJkPxQvoahPn+Ze84WdQW7uCI444gQA3n9/JtOn3wrsBpypLvr0aR6YQqsBBTARkWDnDmIbN8KQIVCrlrPdHcQuvxy++abg8IlrJhYLX27ZedlMWjPJD0VLKCo6Xxg0Ys+eWwD3k5O/AuO55JIwn1NdiIcCmIhIddGsGUyZ4vSIeQexWbPgnHMKgtjOfTtLvczO/aXvFylN8RBWFxgKdHX9nMX8+ffz5ptvBKbAakIBTESkuvEOYjfdVCyIfTQzgja/lXx6gzoN/FKmhK6wMMPkyT29ttQC+gNXEh4eTk5ODoMHD+bee+/l4MGDgSkyyCmAiYhUV82awdSpxYLYZety+OZVeH8GxYJYVHgUw9sPD0CxEkry8y3Dhs3zsSeWiy56nAYNnJD/7LPP0rdvX/7++2//FlgNKICJiFR37iC2cSPEx2NdQeyKHygIYq1/d8JX8/rNSeiaEOCCpTpzTzXhvbC3t88+CyMu7hlatXJuUX766ad07tyZzZv1RKQ3BTARkVDRvDn83/9hNm4kd9BADroGQF/xA3z7Cnw5twmrO75GdGR0gAuV6spX+IqPb0Vu7t1eY8Jg5sxM2rZN4rLL+gCwYcMGOnbsyMKFC/1ec7BSABMRCTXNmxMx7U1qbfyR33r3Lrg1edYXP1C3Qxe48kpYuzbARUp1NHt2RrHwNWVKL8LDw4oMzIfp03/ippue4f777wdg9+7d9OzZk5dffhlrrd9rDzYKYCIioapFCzbedx/88AMMHuwZrP/BB9CmDVx1lYKYVEi/fi1ITHTWg3SHL/dUE0WfjkxM7Mzll5/GE088wVtvvUXt2rU5ePAgt956K8OHDyc3Nzdg7yMYKICJiIS6Fi0gJcUJYoMGeYLY++8riEmFjR3blVmz+vuc58sdwmbN6s/YsV0Ltl933XUsXbqU448/HoBXX32Viy66iMzMTL/WHkwUwEREaooWLWDaNE8QC3P9ClAQkwrq169FiZOshoUZ+vVrUWx7x44dSU9Pp3379gAsWbKEjh07sn79+iqtNVgpgImI1DRlBbGrr4bvvgtoiRKaTjzxRJYuXcqAAQMA2LJlC7GxscyePTvAlfmfApiISE116qmeIHbjjZ4gNnMmtG6tICZVok6dOrz99ts8/vjjAGRlZdGvXz+efvrpGjU4XwFMRKSmO/VUeP31koPYv/8N63zP+SRyKIwxPPDAA8yaNYt69ephrWX06NHceOONZGf7Xsc01CiAiYiIwx3ENmyAG27wBLH//hfOPltBTCpdv379WLlyJU2aNAFg+vTpdO/end9+K2UtrRChACYiIoWddhq88YbvINa6NVxzDdTQgdNS+c4++2xWr15Nt27dAFi9ejUdOnRgzZo1Aa6saimAiYiIb+4g9v33MHCgE8Sshffec3rEFMSkEqSmbqZBg4bMnz+fm2++GYBff/2Vbt268c47M0hNDc0ljBTARESkdKefDm++edhBLCsni8RFicQkxxCWFEZMcgyJixLJysnyw5uQYDR27HL695/F0KFzCQ+P4NVXX2X8+PHUqlWL7OxsrrvuWvr3/w+JiV8EutRKpwAmIiLlU1YQGzCgxCCWlZNF7JRYxq0YR+a+TCyWzH2ZjFsxjtgpsQphNVBq6maSklYCkJKyjqFD52It3HbbbXzyyadEFqxZuoBHHhnBjBnfBq7YKqAAJiIiFeMOYuvXw/XXe4LYu+96gtj33xc6JXl5Mhm7M8jOK/yEW3ZeNhm7M0henuzPdyBBoE+f5oXWjnSHsLy8fN59N5+cnBFAjGvvOp588kZ+/vnngNRaFRTARETk0JxxBkyf7glixniCWKtWcO21BUFs4pqJxcKXW3ZeNpPWTPJn5RIEiq4dCU4Ii4h4zrXgdwxwGyee2A6AtWvX0qFDB5YtWxaYgiuZApiIiBwedxD7/nu47jpPEJsxoyCIHbu19DX/du7f6adiJZj4CmHe4uM78NNPK7nrrrsA+PPPPzn//POZOnWqP8usEgpgIiJSOc44A956y+kRKxLEvpsEb82EM/70fWqDOg38W6sEjbAww+TJPX3umzy5J5GRETz33HNMnTqViIgIcnNzGTp0KHfeeSd5eXl+rrbyKICJiEjlOvNMTxC79lowhjAL162D9S8XD2JR4VEMbz88cPVKQOXnW4YNm+dz37Bh8/jww03k51tuuukmFi5cSEyMMy7sxRdf5JJLLuWtt77yZ7mVRgFMRESqxplnwttvw/r15F5zNfnG+aXjHcTa7Iqkef3mJHRNCHS1EgD5+ZahQ+e6xnwVl5KyjiuuSGXIkDnk51vOPfdc0tPTadOmDQCffz6PgQN7c9tt7/iz7EqhACYiIlXrzDOJmPEe+79OZ+35rQoFsa9eyuHrL1oS/dMvga5S/MxX+IqPb0Vu7t3FxoRNm7a+IISdcsopLF36Baec0tW1908mTBjC2LEpfqz+8CmAiYiIX9Rr057WC74jbN16Z6oK163JiBnvwVlnOU9S/vBDoMsUP5k9O6NY+JoypRfh4WFMmdKLwYNbFjp+2rT1BdNU3Hnncn7+uS9woWvvfh59dCgvvvgi1lr/vYnDoAAmIiL+ddZZ8M47zsLeriCGtc7typYtnUleN26s0hI0K3/g9evXgsTEzoAnfIWFGcAZmD91au9iIazwNBVhQC969LifOnXqkJ+fz5133snNN99MTk6On99NxSmAiYhIYLiD2HffOcsZGQP5+c4A/rPOqrIgpln5g8fYsV2ZNat/ofDl5g5hH3zQr5RpKlqxYMHjfPHFF5x44okATJ06lQsuuIAdO3ZUef2HQwFMREQCq2VLZ86wkoLYDTdUahDTrPzBpV+/FsXCl1tYmOHyy08tdZqKsDBDu3btSE9Pp1OnTgAsW7aMjh07snbt2iqr+3ApgImISHAoKYhNn+4JYj/+eNgvo1n5q5eypqnIz3fGfB1//PEsXryYG264AYCff/6ZLl268OGHH/qt1opQABMRkeDiDmJr18K//104iJ15Jtx442EFsZ37Sp91X7PyB4/yTFMxdOjcghAWFRXF66+/ztNPP40xhr1793LFFVfw2GOPBd3gfAUwEREJTq1aOetKuoMYOEHszTcPK4g1qFv6rPualT84lHeaiqIhzBjDqFGj+Oijj4iOjgbg4Ycf5rrrrmPfvn3+fROlUAATEZHg5g5i330HV1/tbDuMIDai/QiiwqN87tOs/MGjrGkqioaw2bMzCp1/2WWXkZaWRrNmzQCYMWMG5513Hr/++qt/3kAZFMBERKR6aNUK3nuv5CA2aBBs2lTmZRK6JtC8fvNiISwqPEqz8geRsqap8A5hiYmd6devRbFrtGzZklWrVtGjRw8AvvzyS9q3b8+qVav88yZKoQAmIiLVizuIrV1bOIi98YazIHgZQSw6Mpq0oWmM6jKKmLoxhJkwYurGMKrLKNKGphEdGe2nNyJlKWuaiilTejFrVn/Gju1awhWgYcOGzJs3j//85z8A/P7773Tv3p3p06dXae1lUQATEZHq6eyzPUHsqqucbe4gduaZMHgwbN7s89ToyGiS4pLYkbCDg2MOsiNhB0lxSQpfQaisaSp89XwVFRERwaRJk3j55ZepVasWBw4c4IYbbuDVV18lPz+/sksuFwUwERGp3s4+G/7738JB7OBBeP11p0ds8GDqBMm4HwmsESNGMG/ePOrXrw/Anj17MMZ3uKtqCmAiIhIaSgliHW+8EeLjS+wRk5rj/PPPZ/Xq1QwZMoQ77rhDAUxERKRSuIPYt9/ClVcCYPLzYdo0p0dMQazGa9GiBVOmTCEiIiJgNQRFADPG1DLGfG2M+TjQtYiISIho3RpmzoRvv+XP885zth08WDiIZWSUegmRqhIUAQy4A9gQ6CJERCQEtW7N+qQk+OYbuOIKZ5s7iJ1+Otx0k4KY+F3AA5gxpjFwKTAl0LWIiEgIa9MG3n+/eBBLSVEQE78LeAADXgBGAYF5DlRERGoW7yB2+eXONu8gNmQI/PRTQEuUypeaurlguaKi8vMtqan+HRdoArk4pTHmMuASa+0IY0wP4F5r7WU+jhsGDANo1KhRuxkzZvi1zmCTlZVVsL5VTae28FBbeKgtPNQWjtLaIXrzZk554w1ivviiYJsNC+P3Xr34eeBAsk84odg5+w/uZ8a2GaRuT+Wf3H84MuJI+p3QjwEnDaBOrTpV9j4qQ038TEyb9iuvv/4bvXs3ICGhScG8YllZWdStW4/k5K3MmbOTQYOOZ/DgEyv1tePi4r601rYvuj3QAexJ4AYgD4gCjgQ+sNYOLOmc9u3b2zVr1vipwuC0ePHigmUVajq1hYfawkNt4aG2cJSrHb75Bh55BD780LMtPNyZWf/BB6FpUwCycrKInRJLxu4MsvOyCw51L2UU7LPp17TPRGrqZvr3n1Xws/eyRgsXLmL69AOF1pycNat/uSZ3LS9jjM8AFtBbkNba+621ja21TYABwMLSwpeIiEiVadsWPvgAvvoK+vd3tuXlwdSpcNppMHQobNlC8vLkYuELIDsvm4zdGSQvT/Z76VKyPn2aF1u4e+jQueTl5ZOcvLXYgt99+jT3S13BMAZMREQkeJxzjtMLVkIQazH6aY77M9vnqdl52UxaM8l/tUqZii7cDU4Ii4h4jjlzdhZsK7rgd5XX5ZdXKQdr7WJf479EREQCooQgdsPqA/z4Ekz+CE7ZXfy0nft3Ft8oAeUrhHnzd/iCIApgIiIiQck7iPXrB0BEPtz8FWx6CV4tEsQa1GkQoEKlNGFhhsmTe/rcN3lyT7+GL1AAExERKZ9zzoFZs3jllZuZfabz6zMiH4Z5BbHT9kQyvP3wABcqvuTnW4YNm+dz37Bh80qcoqKqhPv11URERKq5gfHPEXtwBU+s38ToBTn02+gJYvHf5MBf26DZz3DKKYEuVVzy8y1Dh84tNODem3t7jRwDJiIiUh1ER0aTNjSNnleN5uYhMXS4xfDZWZGAE8QipqbAqafCLbfAzz8HuFrxFb7i41uRm3s3vXt7bhe7n470V0+YApiIiEgFRUdGkxSXxI6EHaS/ks/F6w/AmjXQp49zQG4uTJ6sIBYEZs/OKBa+pkzpRXh4GAkJTYo9HTl7tn+Wo1IAExERqQzt2sFHH5UcxP7zHwWxAOjXrwWJiZ2B4k87Fn06MjGxc6VOwloaBTAREZHK5A5i6elwmWt2pdxcePVVTxD73/8CW2MNM3ZsV2bN6u9zjJc7hM2a1Z+xY7v6rSYFMBERkarQvj3Mnu07iLVoAcOHK4j5Ub9+LUocYB8WZvzW81Xwmn59NRERkZqmpCD2yisKYjWYApiIiIg/uIPY6tVw6aXONgWxGksBTERExJ86dICPP4bVq8m7uJezzRXEcpqdwup+Hdib8UNga5QqpwAmIiISAFltzqTtZb/Q7T+RfHKqsy3yIHT8aA2Rp59F7i03w7ZtgS1SqowCmIiISAAkL08mY3cGy47L4bLroeNQCoJYxEFLxOQpzq3JkSMVxEKQApiIiEgATFwzkey87IKf0xvDZddDp6HwqfuBvJwcmDhRQSwEKYCJiIgEwM59O31uX90YLh0InW82cPHFzsaiQeyXX/xYqVQFBTAREZEAaFC3Qan7M05tCJ9+CmlpxYNY8+Zw660KYtWYApiIiEgAjGg/gqjwKJ/7osKjGN5+uPNDp05OEFu5Enr3drbl5MDLLyuIVWMKYCIiIgGQ0DWB5vWbFwthUeFRNK/fnISuCYVPiI2Fzz4rOYjddhv8+qufqpfDpQAmIiISANGR0aQNTWNUl1HE1I0hzIQRUzeGUV1GkTY0jejIaN8nuoPYihXQyzWPWE4OTJgAzZopiFUTCmAiIiIBEh0ZTVJcEjsSdnBwzEF2JOwgKS6p5PDlrXNnmDPHdxBr3hxuv11BLIgpgImIiFRn7iC2fDn07OlsO3AAXnrJE8S2bw9sjVKMApiIiEgo6NIF5s71HcSaNYM77lAQCyIKYCIiIqHEHcSWLYOLLnK2HTgA48dDs2a0eOklBbEgoAAmIiISirp2hXnzigWxxh98oB6xIKAAJiIiEspKCGKMH++MEbvzTvjtt4CWWBMpgImIiNQEriD29fjxcOGFzrbsbHjxRadHTEHMrxTAREREapC/zz4bPv8cvvjCdxC7665Sg1hWThaJixKJSY4hLCmMmOQYEhclkpWT5ad3EBoUwERERGqic891gtjSpXDBBc627Gx44YUSg1hWThaxU2IZt2IcmfsysVgy92UybsU4YqfEKoRVgAKYiIhITdatG8yfX3IQu/tu+P13AJKXJ5OxO4PsvOxCl8jOyyZjdwbJy5P9XHz1pQAmIiIiniC2ZAmcf76zLTsbnn8emjaFu+9m5qIJxcKXW3ZeNpPWTPJjwdWbApiIiIh4nHceLFjgM4ilP7mLZ+ZCoz2+T925f6f/6qzmFMBERESkOHcQW7wY4uIAqJsH96yEn17EZxBrUKeB/+usphTAREREpGTdu8PChbB4MT+1bQIUD2LHZkFUeBTD2w8PbK3ViAKYiIiIlK17d45d9R2D72zC4qZOfHAHsS0vwqRF9RjVYlCAi6w+FMBERESkXKIjo5nw9HcsmvoQ/W45ioVNne11c2Hwgp3UO70V3Hsv/PFHYAutBhTAREREpNyiI6NJiksi9ZW/OP8nC4sWQY8ezs79++HZZ52nJhMSYMeOgNYazBTARERE5ND16OGEsEWLnPFi4ASxZ55RECuFApiIiIgcvh49nCcmFy1ynqAE2LdPQawECmAiIiJSeXr0cOYQKymIjRqlIIYCmIiIiFQFd4/YwoXOLPvgBLHkZAUxFMBERESkqhjjTOK6ZEnJQey+++DPPwNbZwAogImIiEjVKi2IjRsHTZrUuCCmACYiIiL+4R3EFiyAc891ttfAIKYAJiIiIv5ljLPQ99KlvoNY06YwenRIBzEFMBERESm3rJwsEhclEpMcQ1hSGDHJMSQuSiQrJ6viF/MOYvPnQ9euzva9e+Hpp0M6iCmAiYiISLlk5WQROyWWcSvGkbkvE4slc18m41aMI3ZK7KGFMHCC2AUXwBdflB7EMjMr780EmAKYiIiIlEvy8mQydmeQnZddaHt2XjYZuzNIXp58eC/gHcQ+/xy6dHG2u4NYkyZw//0hEcQUwERERKRcJq6ZWCx8uWXnZTNpzaTDun7B7c1njiVseU9i+m3k9eSBHOzcyTlg71546qmQCGIKYCIiIlIuO/ftLH3//tL3l8bn7c39O/nPgZm0uX4P+z9Jhc6dnYNDIIgpgImIiEi5NKjboPT9dUrfX5pSb2/+9RNP1fkSli+HefOKB7GmTeGBB6pVEFMAExERkXIZ0X4EUeFRPvdFhUcxvP3wQ752uW5vGgMXXeQEsblzPUEsKwuefNITxHYeek+cvyiAiYiISLkkdE2gef3mxUJYVHgUzes3J6FrwiFfu0K3N42Bnj09QSw21tnuDmJNmsCDDwZ1EFMAExERkXKJjowmbWgao7qMIqZuDGEmjJi6MYzqMoq0oWlER0Yf8rUP6famO4itWFE8iD3xhNMj9tBDsGvXIddVVRTAREREpNyiI6NJiktiR8IODo45yI6EHSTFJR1W+ILDvL3pHcTmzPEEsT174PHHnR6xb789rPoqmwKYiIiIBFyl3N40Bnr18gSxTq7pK44/Hlq2rIKqD50CmIiIiARcpd7edAexlSudIDZ+PISHV13xhyC4qhEREZEay317MykuqXIu6A5iQUg9YCIiIiJ+pgAmIiIi4mcKYCIiIiJ+FtAAZoyJMsasNsZ8a4xZb4yppJu+IiIiIsEr0D1gB4DzrbVtgLZAb2NMbGBLEhERkWCXlZNF4qJEYpJjCEsKIyY5hsRFiWTlZAW6tHIJ6FOQ1loLuFsqwvVlA1eRiIiIBLusnCxip8QWWrw7c18m41aM4/0N7x/2rPz+YJwMFMACjKkFfAm0AF621t7n45hhwDCARo0atZsxY4Z/iwwyWVlZREcH9wfLX9QWHmoLD7WFh9rCoXbwCIW2SNmawoxtM8jJzym2LzIskgEnDWDASQOYsW0GqdtT+Sf3H46MOJJ+J/RjwEkDqFOrDuCftoiLi/vSWtu+6PaABzA3Y8zRwIfAbdbadSUd1759e7tmzRq/1RWMFi9eTI8ePQJdRlBQW3ioLTzUFh5qC4fawSMU2iImOYbMfZkl7m9YpyGNohsV6iEDz6z67h4yf7SFMcZnAAv0GLAC1tq/gMVA78BWIiIiIsFs576dpe7P3J9ZLHwBZOdlk7E7g+TlyVVZXrkE+inIGFfPF8aYOsCFwA+BrElERESCW4O6DUrdbzDFwpdbdl42k9ZMqoqyKiTQPWDHA4uMMWuBdOBza+3HAa5JREREgtiI9iOKLdrtFhUehS3jeb6d+0vvQfOHgAYwa+1aa+051trW1tpW1tpHAlmPiIiIBL+Ergk0r9+8WAhzj/FqUKf0HrKy9vtDoHvARERERCokOjKatKFpjOoyipi6MYSZMGLqxjCqyyjShqYxssPIUnvIhrcf7ueKiwvoPGAiIiIihyI6MpqkuCSS4oovopPQNYH3N7xf4lOQCV0T/FmqT+oBExERkZBSVg9ZMEzSqh4wERERCTml9ZAFA/WAiYiIiPiZApiIiIiInymAiYiIiPiZApiIiIiInymAiYiIiPiZApiIiIiInymAiYiIiPiZApiIiIiInymAiYiIiPiZsdYGuoYKMcb8Cfwc6DoCrCGQGegigoTawkNt4aG28FBbONQOHmoLD3+0xSnW2piiG6tdABMwxqyx1rYPdB3BQG3hobbwUFt4qC0cagcPtYVHINtCtyBFRERE/EwBTERERMTPFMCqp8mBLiCIqC081BYeagsPtYVD7eChtvAIWFtoDJiIiIiIn6kHTERERMTPFMCqEWPMvcYYa4xpWML+rcaY74wx3xhj1vi7Pn8qR1v0NsZsNMZsNsaM9nd9/mCMedQYs9b19z3PGHNCCceF/OeiAm0R0p8LY0yyMeYHV1t8aIw5uoTjasJnorxtEdKfCQBjzNXGmPXGmHxjTIlP/NWQz0V526LKPxcKYNWEMeYk4CLgf2UcGmetbRvKjxiX1RbGmFrAy8DFwFnAtcaYs/xXod8kW2tbW2vbAh8DY0o5NtQ/F2W2RQ35XHwOtLLWtgZ+BO4v5dhQ/0yU2RY15DMBsA64AlhajmND/XNRZlv463OhAFZ9PA+MAjRor+y26Ahsttb+ZK3NAWYA/fxVnL9Ya//x+rEeNfizUc62CPnPhbV2nrU2z/VjGtA4kPUEUjnbIuQ/EwDW2g3W2o2BriMYlLMt/PK5UACrBowxfYFfrbXflnGoBeYZY740xgzzQ2l+V862OBHY5vXzL65tIccY87gxZhtwPSX3gIX85wLK1RY15nPhchPwWQn7asRnwktJbVHTPhNlqWmfi5L45XMRXtkXlENjjJkPHOdj14PAA0DPclymq7V2uzHmWOBzY8wP1trydDkHlUpoC+NjW7XsHSqtLay1qdbaB4EHjTH3A7cCiT6ODfnPRTnbIiQ+F2W1g+uYB4E84K0SLlMjPhOuY0pri5D4TED52qIcasznoqxL+NhW6Z8LBbAgYa290Nd2Y8zZQFPgW2MMON3oXxljOlprfy9yje2uP3cYYz7E6Uatdv94KqEtfgFO8vq5MbC9isqtUiW1hQ9vA5/gI4CF+ufCh5LaIiQ+F2W1gzFmEHAZcIEtYZ6hmvKZKEdbhMRnAir076O0a9SIz0U5+OVzoVuQQc5a+5219lhrbRNrbROcD8a/ioYvY0w9Y8wR7u9xeonW+b3gKlTetgDSgVONMU2NMZHAAOAjP5db5Ywxp3r92Bf4wccxIf+5gPK1BTXgc2GM6Q3cB/S11u4r4Zia8pkosy2oAZ+J8qopn4ty8svnQgGsGjPGnGCM+dT1YyNgmTHmW2A18Im1dk7gqvMv77ZwDby9FZgLbADes9auD2R9VeQpY8w6Y8xanP9Y3gE19nNRZlvUkM/FBOAInNtH3xhjXoEa+5kosy1qyGcCY8zlxphfgM7AJ8aYua7tNe5zUZ628NfnQjPhi4iIiPiZesBERERE/EwBTERERMTPFMBERERE/EwBTERERMTPFMBERERE/EwBTERERMTPFMBERERE/EwBTETEj4xrHS1jzDTvn0WkZtFakCIS8owxtSi8wG6+tTY/QOVcZYxpBdQxxlwGXAyMDFAtIhIg6gETEb8yxgwwxuQYYyIq+brGGPOtawHmojKAXK+vMZX52hVhrf0vzgLH/YErrbXFwpcx5mVjzFR/1yYi/qOliETEr4wxTwIXW2vbVvJ1rwGSgebW2twi+84Gantt2m6t3V6Zr19expirgLOBM4A3gV7W2tuKHNMEZ0HxVtbazX4vUkSqnAKYiPiVMeYzYIe11ldP1eFcdzmw2Fr7YGVet7IZY4y11hpjpllrB7t/9nHcfOBba+09AShTRKqYbkGKiL+1Ab5x/2CMqWuMGWeM+Z8xJssYs9QY08b7BGPMMcaYqcaY3caYTGPM/caYB40xP7j2twC6ADOLvpgxppYx5i5jzFpjTLYx5jdjzFtVMfi9PK/lDlvW2sHeP/vwPnC9MUb/nRYJQRqELyJ+Y4yJAY4HvnX9XAdYCBwFjAYygbuBecaYM6y1u40xtYHPgWjgNuAv4HHgSGC169IXAHvd1/V6vTCcUNYDeAr4EjgJ5xZopXb/V8FrrQAa4dyu/LaMY0WkmlEAExF/auv60x0okoBTgLOttZkAxpgvgT9xng58GyeYnQq0sNbucB3zN85A9tdc12kHbPDxZONdwEVAB2vtBq/tKZX4nqrqtdYDB4GOKICJhBwFMBHxpzbAL9bancaYSGAY8Iw7fAG49v0DnOjqVboVeN4dvly2uP50B5PjcHrPCrjOHQVMKBKIfDLGHIXTO1cqa+0PPs6t0GuVh7U2zxjzF857E5EQowAmIv7UBk9oaoNz6/Fz7wOMMfVc238HWgMNgdlFrnOi68+1rj+jgH1FjmkNHAt8WM7arsbTo1YaX2PHKvpa5XUA572JSIjR4E4R8ae2eAJYQ9efvxc5pofrz2V4eqR2FDnmPGC3tXab6+ddwNFFjnGf+1t5CrPWTrHWmrK+Sji9Qq9VAUfjvDcRCTEKYCLiF65bjmfgeQLSHZ6aeR0TjjNJ6hxr7RY8txVbeB1zFHAnhcdFbQSaFnlJd7A78/CrL1Olv5brgYW6wI+VdU0RCR6aB0xE/MIYcw7wFXC6tfZH19QMa4AI4CEgH2cg+xlArLV2myu0bQb+Ae7HGTbxAM6g/BRr7V2ua/cE5gLHWmv/dG0Lxwl7dXFC3XbgLOAka+19lfzeKv21jDEXA58AMdbanZVUqogECfWAiYi/tMEZp7UZCua/ugL4GXgDmIZzC6+j+9aitTYHZ2xWLvAe8CDwGM7TgV94XXsxzq263u4N1to8oA/wNfA8zjiyoa6fK1UVvVZvYInCl0hoUg+YiFQrxpjbcXrMTrbWZnttfxFnqopLA1ZcJXEtHv4zMNpaOz3Q9YhI5dNTkCIStIwxPXBmuHffqrwEuBkY6B2+XJKBjcaY06y11X3c1NXAfmBGoAsRkaqhACYiwawuMBB4GGeM2BrgMmvtvKIHWmt/McYMwXkisboHMAMMcd3aFJEQpFuQIiIiIn6mQfgiIiIifqYAJiIiIuJnCmAiIiIifqYAJiIiIuJnCmAiIiIifqYAJiIiIuJnCmAiIiIifqYAJiIiIuJnCmAiIiIifvb/IX6J2pVXpckAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(10,6) )\n",
    "\n",
    "plt.plot(xM, yM,'go',markersize = 8)\n",
    "# plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"High traffic behavior\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "plt.plot(xB, yB,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    " #plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "#plt.plot(x, y,'k-.', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "#plt.plot(x, y,'r-.', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xB)\n",
    "y = predict2(x)\n",
    "plt.plot(x, y,'k', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xM)\n",
    "y = predict(x)\n",
    "plt.plot(x, y,'r', linewidth=2.5)\n",
    "\n",
    "# plt.legend([\"\",\"\",\"\",\"\",str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2)),str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)),\n",
    "#             str(round(predict2[1],2))+\"x + \" + str(round(predict2[0],2)),str(round(predict[1],2))+\"x + \" + str(round(predict[0],2))])\n",
    "plt.legend([\"\",\"\", str(round(predict2[1],2))+\"x + \" + str(round(predict2[0],2)),str(round(predict[1],2))+\"x + \" + str(round(predict[0],2))])\n",
    "plt.savefig(\"../september-report-plots/spatial-5-scale-high-traffic.jpg\",bbox_inches='tight')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.80272068, -4.44266862, -4.06778941, -3.95545738, -3.62058387,\n",
       "       -3.60824318, -3.34756286, -3.33139303, -3.13656397, -3.11225706,\n",
       "       -2.73390425, -2.68068271, -2.48619296, -2.2096253 , -1.95169807,\n",
       "       -1.83302559, -1.6927616 , -1.35575057, -1.35546226, -1.18810709,\n",
       "       -1.10664626, -1.04559912])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2544b5c3a20>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(10,6) )\n",
    "\n",
    "# plt.plot(xM, yM,'go',markersize = 8)\n",
    "plt.plot(xM2, yM2,'go',markersize = 8)\n",
    "plt.ylabel(\"Log Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Log Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "plt.grid(True)\n",
    "# plt.plot(xB, yB,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "plt.plot(xB2, yB2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "\n",
    "predict2_2 = np.poly1d(pB)\n",
    "x  = np.array(xB2)\n",
    "y = predict2_2(x)\n",
    "plt.plot(x, y,'k-.', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xM2)\n",
    "y = predict_2(x)\n",
    "plt.plot(x, y,'r-.', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xB)\n",
    "y = predict2(x)\n",
    "# plt.plot(x, y,'k', linewidth=2.5)\n",
    "\n",
    "x  = np.array(xM)\n",
    "y = predict(x)\n",
    "# plt.plot(x, y,'r', linewidth=2.5)\n",
    "\n",
    "# plt.legend([\"\",\"\",\"\",\"\",str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2)),str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2)),\n",
    "#             str(round(predict2[1],2))+\"x + \" + str(round(predict2[0],2)),str(round(predict[1],2))+\"x + \" + str(round(predict[0],2))])\n",
    "plt.legend([\"\",\"\", str(round(predict2_2[1],2))+\"x + \" + str(round(predict2_2[0],2)), str(round(predict_2[1],2))+\"x + \" + str(round(predict_2[0],2))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected cost for c = 0 case: 3.857\n",
      "[[1.41421356 2.23606798 3.16227766 4.12310563 5.09901951 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 4.12310563 4.47213595 5.\n",
      "  5.65685425 6.40312424 5.09901951 5.38516481 5.83095189 6.40312424\n",
      "  7.07106781]\n",
      " [2.23606798 1.41421356 2.23606798 3.16227766 4.12310563 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.         5.65685425 5.38516481 5.09901951 5.38516481 5.83095189\n",
      "  6.40312424]\n",
      " [3.16227766 2.23606798 1.41421356 2.23606798 3.16227766 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         4.47213595 4.12310563\n",
      "  4.47213595 5.         5.83095189 5.38516481 5.09901951 5.38516481\n",
      "  5.83095189]\n",
      " [4.12310563 3.16227766 2.23606798 1.41421356 2.23606798 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 5.65685425 5.         4.47213595\n",
      "  4.12310563 4.47213595 6.40312424 5.83095189 5.38516481 5.09901951\n",
      "  5.38516481]\n",
      " [5.09901951 4.12310563 3.16227766 2.23606798 1.41421356 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 6.40312424 5.65685425 5.\n",
      "  4.47213595 4.12310563 7.07106781 6.40312424 5.83095189 5.38516481\n",
      "  5.09901951]\n",
      " [2.23606798 2.82842712 3.60555128 4.47213595 5.38516481 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 5.09901951 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 3.16227766 3.60555128 4.24264069\n",
      "  5.         5.83095189 4.12310563 4.47213595 5.         5.65685425\n",
      "  6.40312424]\n",
      " [2.82842712 2.23606798 2.82842712 3.60555128 4.47213595 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 4.12310563 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  5.65685425]\n",
      " [3.60555128 2.82842712 2.23606798 2.82842712 3.60555128 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 3.16227766 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.24264069 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         4.47213595 4.12310563 4.47213595\n",
      "  5.        ]\n",
      " [4.47213595 3.60555128 2.82842712 2.23606798 2.82842712 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 2.23606798 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 5.65685425 5.         4.47213595 4.12310563\n",
      "  4.47213595]\n",
      " [5.38516481 4.47213595 3.60555128 2.82842712 2.23606798 5.09901951\n",
      "  4.12310563 3.16227766 2.23606798 1.41421356 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.83095189 5.         4.24264069\n",
      "  3.60555128 3.16227766 6.40312424 5.65685425 5.         4.47213595\n",
      "  4.12310563]\n",
      " [3.16227766 3.60555128 4.24264069 5.         5.83095189 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 5.38516481 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 5.09901951 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 3.16227766 3.60555128 4.24264069 5.\n",
      "  5.83095189]\n",
      " [3.60555128 3.16227766 3.60555128 4.24264069 5.         2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 4.47213595 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 4.12310563 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 3.60555128 3.16227766 3.60555128 4.24264069\n",
      "  5.        ]\n",
      " [4.24264069 3.60555128 3.16227766 3.60555128 4.24264069 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 3.60555128 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 3.16227766 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.24264069 3.60555128 3.16227766 3.60555128\n",
      "  4.24264069]\n",
      " [5.         4.24264069 3.60555128 3.16227766 3.60555128 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 2.82842712 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 2.23606798 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 5.         4.24264069 3.60555128 3.16227766\n",
      "  3.60555128]\n",
      " [5.83095189 5.         4.24264069 3.60555128 3.16227766 5.38516481\n",
      "  4.47213595 3.60555128 2.82842712 2.23606798 5.09901951 4.12310563\n",
      "  3.16227766 2.23606798 1.41421356 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.83095189 5.         4.24264069 3.60555128\n",
      "  3.16227766]\n",
      " [4.12310563 4.47213595 5.         5.65685425 6.40312424 3.16227766\n",
      "  3.60555128 4.24264069 5.         5.83095189 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 5.38516481 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563 5.09901951 2.23606798 2.82842712 3.60555128 4.47213595\n",
      "  5.38516481]\n",
      " [4.47213595 4.12310563 4.47213595 5.         5.65685425 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 5.         2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 4.47213595 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766 4.12310563 2.82842712 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595]\n",
      " [5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.24264069 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 3.60555128 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798 3.16227766 3.60555128 2.82842712 2.23606798 2.82842712\n",
      "  3.60555128]\n",
      " [5.65685425 5.         4.47213595 4.12310563 4.47213595 5.\n",
      "  4.24264069 3.60555128 3.16227766 3.60555128 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 2.82842712 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356 2.23606798 4.47213595 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712]\n",
      " [6.40312424 5.65685425 5.         4.47213595 4.12310563 5.83095189\n",
      "  5.         4.24264069 3.60555128 3.16227766 5.38516481 4.47213595\n",
      "  3.60555128 2.82842712 2.23606798 5.09901951 4.12310563 3.16227766\n",
      "  2.23606798 1.41421356 5.38516481 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798]\n",
      " [5.09901951 5.38516481 5.83095189 6.40312424 7.07106781 4.12310563\n",
      "  4.47213595 5.         5.65685425 6.40312424 3.16227766 3.60555128\n",
      "  4.24264069 5.         5.83095189 2.23606798 2.82842712 3.60555128\n",
      "  4.47213595 5.38516481 1.41421356 2.23606798 3.16227766 4.12310563\n",
      "  5.09901951]\n",
      " [5.38516481 5.09901951 5.38516481 5.83095189 6.40312424 4.47213595\n",
      "  4.12310563 4.47213595 5.         5.65685425 3.60555128 3.16227766\n",
      "  3.60555128 4.24264069 5.         2.82842712 2.23606798 2.82842712\n",
      "  3.60555128 4.47213595 2.23606798 1.41421356 2.23606798 3.16227766\n",
      "  4.12310563]\n",
      " [5.83095189 5.38516481 5.09901951 5.38516481 5.83095189 5.\n",
      "  4.47213595 4.12310563 4.47213595 5.         4.24264069 3.60555128\n",
      "  3.16227766 3.60555128 4.24264069 3.60555128 2.82842712 2.23606798\n",
      "  2.82842712 3.60555128 3.16227766 2.23606798 1.41421356 2.23606798\n",
      "  3.16227766]\n",
      " [6.40312424 5.83095189 5.38516481 5.09901951 5.38516481 5.65685425\n",
      "  5.         4.47213595 4.12310563 4.47213595 5.         4.24264069\n",
      "  3.60555128 3.16227766 3.60555128 4.47213595 3.60555128 2.82842712\n",
      "  2.23606798 2.82842712 4.12310563 3.16227766 2.23606798 1.41421356\n",
      "  2.23606798]\n",
      " [7.07106781 6.40312424 5.83095189 5.38516481 5.09901951 6.40312424\n",
      "  5.65685425 5.         4.47213595 4.12310563 5.83095189 5.\n",
      "  4.24264069 3.60555128 3.16227766 5.38516481 4.47213595 3.60555128\n",
      "  2.82842712 2.23606798 5.09901951 4.12310563 3.16227766 2.23606798\n",
      "  1.41421356]]\n"
     ]
    }
   ],
   "source": [
    "file_name = \"../longest_spatial_uniform_25_all_good.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "        M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "Q_paths_M = M_res[\"Q_paths\"]\n",
    "C_paths_M = M_res[\"C_paths\"]\n",
    "Q_paths_B = B_res[\"Q_paths\"]\n",
    "C_paths_B = B_res[\"C_paths\"]\n",
    "(average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M)\n",
    "(average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B)\n",
    "[Ex,fluid_sol] = run_extremes(N,W,pmf_cust,pmf_serv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_name = \"../sim_paths_sp_u_large_queue_25_2.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "        B_res2_2, N2_2, W2_2, pmf_cust2_2, pmf_serv2_2 = pickle.load(f)\n",
    "Q_paths_B = B_res2_2[\"Q_paths\"]\n",
    "C_paths_B = B_res2_2[\"C_paths\"]\n",
    "(average_cost_B2_2, average_queue_B2_2) = utils.average_paths(C_paths_B,Q_paths_B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_name = \"../sim_paths_sp_u_large_queue_25.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "        B_res2, N2, W2, pmf_cust2, pmf_serv2 = pickle.load(f)\n",
    "Q_paths_B = B_res2[\"Q_paths\"]\n",
    "C_paths_B = B_res2[\"C_paths\"]\n",
    "(average_cost_B2, average_queue_B2) = utils.average_paths(C_paths_B,Q_paths_B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.07804063, 0.04710934, 0.03814478, 0.0252374 , 0.02257238,\n",
       "       0.01325665, 0.02636422, 0.01404428, 0.02024756, 0.01582395,\n",
       "       0.01121125, 0.0091658 , 0.00843533, 0.00769769, 0.00709842,\n",
       "       0.01018333, 0.01604681, 0.01743548, 0.01215235, 0.00964069,\n",
       "       0.01364361])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_cost_B2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.08230634, 0.04289132, 0.03741056, 0.02520653, 0.02498381,\n",
       "       0.02149859, 0.03004581, 0.01496662, 0.01472831, 0.01907808,\n",
       "       0.00999109, 0.01157144, 0.01622589, 0.00957975, 0.00699481,\n",
       "       0.01668105, 0.01413628, 0.01022676, 0.01185989, 0.00977118,\n",
       "       0.01203922])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_cost_B2_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B2 == average_queue_B2_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5.46600944  8.95367098  1.92482602  0.12232539 10.68308258 62.17206426\n",
      " 13.96434232  6.56733534 27.25884101 20.56460203 10.88334234 26.24580803\n",
      " 92.35622669 24.44967165  1.45968939 63.80744891 11.90599319 41.34511077\n",
      "  2.4066518   1.3535355  11.75933104]\n"
     ]
    }
   ],
   "source": [
    "percent_change = 100*np.divide(abs(average_cost_B2_2-average_cost_B2),average_cost_B2)\n",
    "print(percent_change)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Different!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "dict = {\"queue\": average_queue_B2, \"average_cost_1\": average_cost_B2,\"average_cost_2\":average_cost_B2_2,\"percent_change\":percent_change}\n",
    "df = pd.DataFrame(data=dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>queue</th>\n",
       "      <th>average_cost_1</th>\n",
       "      <th>average_cost_2</th>\n",
       "      <th>percent_change</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1194.1</td>\n",
       "      <td>0.078041</td>\n",
       "      <td>0.082306</td>\n",
       "      <td>5.466009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3632.1</td>\n",
       "      <td>0.047109</td>\n",
       "      <td>0.042891</td>\n",
       "      <td>8.953671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6154.1</td>\n",
       "      <td>0.038145</td>\n",
       "      <td>0.037411</td>\n",
       "      <td>1.924826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8414.5</td>\n",
       "      <td>0.025237</td>\n",
       "      <td>0.025207</td>\n",
       "      <td>0.122325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10576.5</td>\n",
       "      <td>0.022572</td>\n",
       "      <td>0.024984</td>\n",
       "      <td>10.683083</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     queue  average_cost_1  average_cost_2  percent_change\n",
       "0   1194.1        0.078041        0.082306        5.466009\n",
       "1   3632.1        0.047109        0.042891        8.953671\n",
       "2   6154.1        0.038145        0.037411        1.924826\n",
       "3   8414.5        0.025237        0.025207        0.122325\n",
       "4  10576.5        0.022572        0.024984       10.683083"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>queue</th>\n",
       "      <th>average_cost_1</th>\n",
       "      <th>average_cost_2</th>\n",
       "      <th>percent_change</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>26538.10000</td>\n",
       "      <td>0.008435</td>\n",
       "      <td>0.016226</td>\n",
       "      <td>92.356227</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>32508.10000</td>\n",
       "      <td>0.010183</td>\n",
       "      <td>0.016681</td>\n",
       "      <td>63.807449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>12846.10000</td>\n",
       "      <td>0.013257</td>\n",
       "      <td>0.021499</td>\n",
       "      <td>62.172064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>38988.10000</td>\n",
       "      <td>0.017435</td>\n",
       "      <td>0.010227</td>\n",
       "      <td>41.345111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>19133.30000</td>\n",
       "      <td>0.020248</td>\n",
       "      <td>0.014728</td>\n",
       "      <td>27.258841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>25548.10000</td>\n",
       "      <td>0.009166</td>\n",
       "      <td>0.011571</td>\n",
       "      <td>26.245808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>28028.10000</td>\n",
       "      <td>0.007698</td>\n",
       "      <td>0.009580</td>\n",
       "      <td>24.449672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>22603.30000</td>\n",
       "      <td>0.015824</td>\n",
       "      <td>0.019078</td>\n",
       "      <td>20.564602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>15786.10000</td>\n",
       "      <td>0.026364</td>\n",
       "      <td>0.030046</td>\n",
       "      <td>13.964342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>35498.10000</td>\n",
       "      <td>0.016047</td>\n",
       "      <td>0.014136</td>\n",
       "      <td>11.905993</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>49999.50001</td>\n",
       "      <td>0.013644</td>\n",
       "      <td>0.012039</td>\n",
       "      <td>11.759331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>25058.10000</td>\n",
       "      <td>0.011211</td>\n",
       "      <td>0.009991</td>\n",
       "      <td>10.883342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10576.50000</td>\n",
       "      <td>0.022572</td>\n",
       "      <td>0.024984</td>\n",
       "      <td>10.683083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3632.10000</td>\n",
       "      <td>0.047109</td>\n",
       "      <td>0.042891</td>\n",
       "      <td>8.953671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>17163.30000</td>\n",
       "      <td>0.014044</td>\n",
       "      <td>0.014967</td>\n",
       "      <td>6.567335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1194.10000</td>\n",
       "      <td>0.078041</td>\n",
       "      <td>0.082306</td>\n",
       "      <td>5.466009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>42978.10000</td>\n",
       "      <td>0.012152</td>\n",
       "      <td>0.011860</td>\n",
       "      <td>2.406652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6154.10000</td>\n",
       "      <td>0.038145</td>\n",
       "      <td>0.037411</td>\n",
       "      <td>1.924826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>30018.10000</td>\n",
       "      <td>0.007098</td>\n",
       "      <td>0.006995</td>\n",
       "      <td>1.459689</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>47468.10000</td>\n",
       "      <td>0.009641</td>\n",
       "      <td>0.009771</td>\n",
       "      <td>1.353535</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8414.50000</td>\n",
       "      <td>0.025237</td>\n",
       "      <td>0.025207</td>\n",
       "      <td>0.122325</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          queue  average_cost_1  average_cost_2  percent_change\n",
       "12  26538.10000        0.008435        0.016226       92.356227\n",
       "15  32508.10000        0.010183        0.016681       63.807449\n",
       "5   12846.10000        0.013257        0.021499       62.172064\n",
       "17  38988.10000        0.017435        0.010227       41.345111\n",
       "8   19133.30000        0.020248        0.014728       27.258841\n",
       "11  25548.10000        0.009166        0.011571       26.245808\n",
       "13  28028.10000        0.007698        0.009580       24.449672\n",
       "9   22603.30000        0.015824        0.019078       20.564602\n",
       "6   15786.10000        0.026364        0.030046       13.964342\n",
       "16  35498.10000        0.016047        0.014136       11.905993\n",
       "20  49999.50001        0.013644        0.012039       11.759331\n",
       "10  25058.10000        0.011211        0.009991       10.883342\n",
       "4   10576.50000        0.022572        0.024984       10.683083\n",
       "1    3632.10000        0.047109        0.042891        8.953671\n",
       "7   17163.30000        0.014044        0.014967        6.567335\n",
       "0    1194.10000        0.078041        0.082306        5.466009\n",
       "18  42978.10000        0.012152        0.011860        2.406652\n",
       "2    6154.10000        0.038145        0.037411        1.924826\n",
       "14  30018.10000        0.007098        0.006995        1.459689\n",
       "19  47468.10000        0.009641        0.009771        1.353535\n",
       "3    8414.50000        0.025237        0.025207        0.122325"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_df = df.sort_values(by=\"percent_change\",ascending=False)\n",
    "sorted_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_cost = np.append( average_cost_B, average_cost_B2)\n",
    "new_queue = np.append( average_queue_B, average_queue_B2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x190ada936a0>]"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(new_cost, new_queue, 'x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x18fa72470f0>]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(average_cost_B2, average_queue_B2, 'x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(10,6) ) \n",
    "\n",
    "# C = 0 Case\n",
    "\n",
    "# C = Inf/Fluid Case\n",
    "# ylim = max( max( average_queue_B ), max( average_queue_M ) )\n",
    "\n",
    "# plt.plot([fluid_sol['Cost'],fluid_sol['Cost']],[0,ylim],linewidth = 3)\n",
    "# Batching data\n",
    "plt.plot(average_cost_B2,average_queue_B2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "plt.plot(average_cost_B2_2,average_queue_B2_2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkgreen\")\n",
    "# Max Weight data\n",
    "# plt.plot(average_cost_M, average_queue_M,'go',markersize = 8)\n",
    "# plt.plot([Ex],[1],'r*',markersize = 12, markeredgewidth=3)\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "# plt.legend(['Fluid', 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "# plt.legend([ 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1194.1"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(average_queue_B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  2500   4000   5000  10000  15000  20000  25000  30000  35000  40000\n",
      "  45000  50000  55000  60000  65000  70000  75000  80000  85000  90000\n",
      "  95000 100000]\n"
     ]
    }
   ],
   "source": [
    "Tbatches = np.array([2500, 4000])\n",
    "Tbatches = np.append(Tbatches,np.arange(5000, 100001, 5000))\n",
    "print(Tbatches)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "file_name = \"../sim_paths_sp_u_large_queue_25_new.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "        average_cost_B2, average_queue_B2, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "\n",
    "file_name = \"../sim_paths_sp_u_large_queue_25_2.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "        average_cost_B2_2, average_queue_B2_2, N, W, pmf_cust, pmf_serv = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_queue_B2_2 == average_queue_B2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.57290951  0.63115541  4.63143457  0.97337798  1.48477133  4.86955967\n",
      "  0.35226172  2.64309016  2.91356481  4.33232331  1.30381107  1.17598446\n",
      "  2.1858096   6.66062583  0.47245332  2.39152997  9.17803573  3.14276676\n",
      " 12.17520565 19.77478883 11.64206095 13.08310831]\n"
     ]
    }
   ],
   "source": [
    "percent_change = 100*np.divide(abs(average_cost_B2_2-average_cost_B2),average_cost_B2)\n",
    "print(percent_change)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Very reasonable errors! Can also see some increase with Tbatch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.08141537, 0.06617671, 0.05721822, 0.04080267, 0.03337386,\n",
       "       0.02833794, 0.02488942, 0.02304377, 0.0213082 , 0.02027787,\n",
       "       0.0194358 , 0.01709122, 0.01740822, 0.01593996, 0.01570136,\n",
       "       0.01543548, 0.01523136, 0.01416687, 0.0147829 , 0.01428668,\n",
       "       0.01397862, 0.01231621])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_cost_B2_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "Q_paths_B = B_res2_2[\"Q_paths\"]\n",
    "C_paths_B = B_res2_2[\"C_paths\"]\n",
    "(average_cost_B2_2, average_queue_B2_2) = utils.average_paths(C_paths_B,Q_paths_B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(10,6) ) \n",
    "\n",
    "# C = 0 Case\n",
    "\n",
    "# C = Inf/Fluid Case\n",
    "# ylim = max( max( average_queue_B ), max( average_queue_M ) )\n",
    "\n",
    "# plt.plot([fluid_sol['Cost'],fluid_sol['Cost']],[0,ylim],linewidth = 3)\n",
    "# Batching data\n",
    "plt.plot(average_cost_B2,average_queue_B2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "plt.plot(average_cost_B2_2,average_queue_B2_2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkgreen\")\n",
    "# Max Weight data\n",
    "# plt.plot(average_cost_M, average_queue_M,'go',markersize = 8)\n",
    "# plt.plot([Ex],[1],'r*',markersize = 12, markeredgewidth=3)\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "# plt.legend(['Fluid', 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "# plt.legend([ 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q_paths_B = np.transpose( np.asarray(Q_paths_B) )\n",
    "C_paths_B = np.transpose(np.asarray(C_paths_B) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100000"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_paths_B.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.07930958, 0.04897021, 0.0384524 , 0.02900851, 0.02519239,\n",
       "       0.01612731, 0.02712368, 0.01877578, 0.02387684, 0.01669193,\n",
       "       0.02139552, 0.0159683 , 0.01351816, 0.0114209 , 0.00980445,\n",
       "       0.01315676, 0.01947429, 0.01994906, 0.0131519 , 0.00989804,\n",
       "       0.01364375])"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(C_paths_B,axis=0)/(Q_paths_B.shape[0] - Q_paths_B[-1,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.07804063, 0.04710934, 0.03814478, 0.0252374 , 0.02257238,\n",
       "       0.01325665, 0.02636422, 0.01404428, 0.02024756, 0.01582395,\n",
       "       0.01121125, 0.0091658 , 0.00843533, 0.00769769, 0.00709842,\n",
       "       0.01018333, 0.01604681, 0.01743548, 0.01215235, 0.00964069,\n",
       "       0.01364361])"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.average(C_paths_B,axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(10,6) ) \n",
    "\n",
    "# C = 0 Case\n",
    "\n",
    "# C = Inf/Fluid Case\n",
    "# ylim = max( max( average_queue_B ), max( average_queue_M ) )\n",
    "\n",
    "# plt.plot([fluid_sol['Cost'],fluid_sol['Cost']],[0,ylim],linewidth = 3)\n",
    "# Batching data\n",
    "plt.plot(average_cost_B2,average_queue_B2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "plt.plot(average_cost_B,average_queue_B,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkgreen\")\n",
    "# Max Weight data\n",
    "# plt.plot(average_cost_M, average_queue_M,'go',markersize = 8)\n",
    "# plt.plot([Ex],[1],'r*',markersize = 12, markeredgewidth=3)\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "# plt.legend(['Fluid', 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "# plt.legend([ 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.08271642, 0.06576166, 0.05999694, 0.04120374, 0.03387685,\n",
       "       0.02702208, 0.02497741, 0.02366937, 0.02194766, 0.02119615,\n",
       "       0.01918565, 0.0172946 , 0.01703585, 0.01707743, 0.01562753,\n",
       "       0.01507496, 0.01395094, 0.01462655, 0.0131784 , 0.01192795,\n",
       "       0.01252093, 0.01089129])"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_cost_B2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([399.84006397, 249.93751562, 199.960008  ,  99.990001  ,\n",
       "        66.88515818,  49.99750012,  39.99840006,  33.55592094,\n",
       "        28.81761333,  24.99937502,  22.39591499,  19.99960001,\n",
       "        18.33146963,  16.89160656,  15.62475586,  14.49254359,\n",
       "        13.55913818,  12.75493935,  11.94728856,  11.21063665,\n",
       "        10.78155492,   9.9999    ])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1e6/(average_queue_B2*2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_cost2 = average_cost_B2*(np.floor(1e6/(average_queue_B2*2))+1)/(np.floor(1e6/(average_queue_B2*2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.08292373, 0.06602576, 0.06029843, 0.04161994, 0.03439014,\n",
       "       0.02757355, 0.02561786, 0.02438663, 0.02273151, 0.02207932,\n",
       "       0.02005773, 0.01820484, 0.01798229, 0.01814477, 0.01666937,\n",
       "       0.01615174, 0.01502408, 0.01584542, 0.01437644, 0.01301231,\n",
       "       0.01377302, 0.01210144])"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_cost2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x190831b2588>]"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(average_cost_B, average_queue_B,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "[Ex,fluid_sol] = run_extremes(N, W, pmf_cust, pmf_serv)\n",
    "Cstar = fluid_sol['Cost']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "\n",
    "# Get the sorted indices of x\n",
    "sorted_indices = np.argsort(average_cost_B2)\n",
    "\n",
    "# Sort x and reorder y accordingly\n",
    "average_cost_B = average_cost_B2[sorted_indices]\n",
    "average_queue_B = average_queue_B2[sorted_indices]\n",
    "\n",
    "\n",
    "\n",
    "xB = np.log(average_cost_B2 - Cstar)\n",
    "yB = np.log(average_queue_B2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.87903617  2.52646931] [0.1412136]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pB, resB, _, _, _ = np.polyfit(xB, yB, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2 = np.poly1d(pB)\n",
    "x  = np.array(xB)\n",
    "y = predict2(x)\n",
    "plt.figure(figsize=(10,6))\n",
    "plt.legend([\"Batching points\",str(round(predict2[1],2))+\"x + \" + str(round(predict2[0],2)),])\n",
    "plt.plot(xB, yB,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.legend([\"Batching points\",str(round(predict2[1],2))+\"x + \" + str(round(predict2[0],2)),])\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"../longest_spatial_uniform_25_all_good.pkl\",'rb') as f:\n",
    "    M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "\n",
    "Q_paths_M = M_res[\"Q_paths\"]\n",
    "C_paths_M = M_res[\"C_paths\"]\n",
    "Q_paths_B = B_res[\"Q_paths\"]\n",
    "C_paths_B = B_res[\"C_paths\"]\n",
    "(average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M)\n",
    "(average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B)\n",
    "# Get the sorted indices of x\n",
    "sorted_indices = np.argsort(average_cost_B)\n",
    "\n",
    "# Sort x and reorder y accordingly\n",
    "average_cost_B = average_cost_B[sorted_indices]\n",
    "average_queue_B = average_queue_B[sorted_indices]\n",
    "\n",
    "file_name = \"../large_queue_25.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "        average_cost_B2_, average_queue_B2, average_cost_B2,  N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "\n",
    "file_name = \"../large_queue_25_2.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "        average_cost_B2_2_, average_queue_B2_2, average_cost_B2_2, N, W, pmf_cust, pmf_serv = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.43195109  3.91307795  2.76332425  0.85910237  1.43844484  0.71015278\n",
      "  1.63634772  7.24971188  7.20725366  6.24178704  4.90830559 21.10042227\n",
      "  6.77644694  4.31138196  2.14680265  5.05846516 18.55774693  9.41600708\n",
      " 23.90107839 13.21070936 10.12872055  0.933933  ]\n"
     ]
    }
   ],
   "source": [
    "percent_change = 100*np.divide(abs(average_cost_B2_2_-average_cost_B2_),average_cost_B2_)\n",
    "print(percent_change)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "\n",
    "# Get the sorted indices of x\n",
    "sorted_indices = np.argsort(average_cost_B2)\n",
    "\n",
    "# Sort x and reorder y accordingly\n",
    "average_cost_B = average_cost_B2[sorted_indices]\n",
    "average_queue_B = average_queue_B2[sorted_indices]\n",
    "\n",
    "\n",
    "\n",
    "xB = np.log(average_cost_B2 - Cstar)\n",
    "yB = np.log(average_queue_B2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Polynomial fit\n",
    "deg = 1\n",
    "\n",
    "# Get the sorted indices of x\n",
    "sorted_indices = np.argsort(average_cost_B2)\n",
    "\n",
    "# Sort x and reorder y accordingly\n",
    "average_cost_B2 = average_cost_B2[sorted_indices]\n",
    "average_queue_B2 = average_queue_B2[sorted_indices]\n",
    "\n",
    "\n",
    "\n",
    "xB = np.log(average_cost_B2 - Cstar)\n",
    "yB = np.log(average_queue_B2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diag(W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.98643165  2.20911578] [0.17837283]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pB, resB, _, _, _ = np.polyfit(xB, yB, 1, full=True)\n",
    "print(pB,resB)\n",
    "predict2 = np.poly1d(pB)\n",
    "x  = np.array(xB)\n",
    "y = predict2(x)\n",
    "plt.figure(figsize=(10,6))\n",
    "plt.legend([\"Batching points\",str(round(predict2[1],2))+\"x + \" + str(round(predict2[0],2)),])\n",
    "plt.plot(xB, yB,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "plt.plot(x, y,'r')\n",
    "plt.ylabel(r\"$log(\\bar{q})$\", weight='bold',fontsize=15)\n",
    "plt.xlabel(r\"$log(\\bar{c}-c^*)$\", weight='bold',fontsize=15)\n",
    "plt.title(\"Log-Log Plot\", weight='bold',fontsize=15)\n",
    "plt.legend([\"Batching points\",str(round(predict2[1],2))+\"x + \" + str(round(predict2[0],2)),])\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zdJYnIiIiDa7W69idB1xtZqcBvwQ+BuDuD5jZ1cCDwDBwhrvvCPc5HbgU2B24MXwAXAx8z8yGCEbqTpmuL1FQWKcOGAlxvb0bx9w3tr19Pj09SysuiSIiIiIyGdMe7Nx9HbAufL4VOK7C+84Fzi3Tficwv0z7HwmDYS2VC3fFFOpEREQkLrqlWAwSCaO7e0nZbd3dSxTqREREJBYKdjHI553OzjVlt3V2rqm4FIqIiIjIVCjYVVlh9mu507AQnJ7t6FitcCciIiJVp2BXReVCXXv7fLZvP3PUbFmFOxEREYmDgl0V9fdvGhXq2tpm0dOzlKamBD09S8eEu/7+TbUoU0RERBqUgl0VpVItdHUtBIKRuhUr5o5MlCjMli2Eu66uhTNicWIRERGZPrVex67hZDKLaG2dTTLZzPr1t47aVgh3qVSLQp2IiIhUnUbsRERERBqEgl2VZTIbSKf7yk6OKEyuSKf7yGQ21KhCERERaVQKdlWUyw2RzQ4CweSIlSs3j4S70hmz2ewgudxQzWoVERGRxqNgV0XJZPOoma8DA1vp6FjN8HC+7DIoyWRzLcoUERGRBhVp8oSZNQGfAlqBPYo2ubufFkdh9ajcfWJ7ezeOWaxY94sVERGROESdFdsLfCJ8XpxGHFCwK1Iu3BVTqBMREZG4RA12KeBl4GrgBYJAJxUkEkZ395Kywa67e4lCnYiIiMQiarB7Cvipu/9NnMU0inze6excU3ZbZ+cajdiJiIhILCoGOzN7S9HL/wS+bGYnAfcAw4UN7v7L2KqrQ+XuF1us0K5wJyIiItU23qzYx4se3cB+wDXAo0Xtj8VdYD0pF+ra2+ezffuZY+4TW26dOxEREZGpGC/YWYSHlksp0t+/aVSoa2ubRU/PUpqaEqPuEwtBuOvv31SLMkVERKRBVQxm7p6I8pjOYl/rUqkWuroWAsFI3YoVc0dOtxZmyxbCXVfXQt0vVkRERKoq6jp2a4Fr3P2iorYTgcXu/rm4iqtHmcwiWltnk0w2s379raO2FcJdKtWiUCciIiJVF3XEbTEwr6TtGOCzVa2mQaRSLRUnRiQSplAnIiIisRg32JnZJWZ2SfhySeG1mV0KnAL8Ie4C61EuN1RxYkQ+77pHrIiIiMRiohG75cAyggWJDw1fLwc+TTBLdn18pdWnTGYD6XRf2VmvhVmz6XQfmcyGGlUoIiIijWqia+yy4d8u4HZgIHy9A3iSYPkTCeVyQ2Szg0Aw63XLllksXuwkEjZmKZRsdpDW1tk6LSsiIiJVM26wc/csgJkBDLp7+dspCADJZDPt7fNHwtvAwFY6OlbT3b2Ezs41Y9a3Syaba1WqiIiINKCotxS7G3i9mX20pP1l4Bfu/nh1y6pPhVmv8OodJnp7N465C0V7+3zdeUJERESqLmqw6yO4zq4sM/sR8El3f6kaRdWzcuGumEKdiIiIxCXqcie/JAh2O4Bnwr8O/Dr8+xHgX+MosB4lEkZ395Ky27q7lyjUiYiISCyiBrsLgQeAN7v7m4E3h6+/ARxMcP/YdAz11aV83unsLH85YmfnGt0jVkRERGIRNdj9M3C/u/8GIPx7P/DP7v4r4CrgLfGUWF9KZ7+W6u3dWHYpFBEREZGpihrs/gicYmY9ZvZ5M/su8HHg9+H2fYFtcRRYT8qFuvb2+WzffubIPWJB4U5ERETiETXYfSV8bzvwVeAzBBMvvmJmbwQ+DKyLo8B60t+/aVSoa2ubRU/PUpqaEvT0LB0T7vr7N9WiTBEREWlQkWbFuvu3zexB4FSC6+t+BXzP3Qt3ntCCbAT3iO3qWkg2O0h7+3xOPXW3kYkSpbNlu7oWanFiERERqaqoy53g7uvQqNyEMplFtLbOJplsZv36W0dtK4S7VKpFoU5ERESqLlKwM7O9gDOBVmCPok3u7sfFUVg9Gy+0JRKmUCciIiKxiDpi919AG1C6AJuu/hcRERF5jYga7D4APEewnt0LKNCNK5cbqngf2Hze6e/fpFE7ERERqbqos2J/Adzg7hl3/4a7/7/CI87i6lEms4F0uq/sciaF5VDS6T4ymQ01qlBEREQaVdQRu6uAL5jZ/cA9wHBhQ9HM2Bkvlxsimx0EgpmvW7bMYvFiJ5GwMWvcZbODtLbO1sidiIiIVM3OrGO3O7ASuAm4JXysjamuupRMNo9aq25gYCsdHasZHs6XXbi40ulaERERkcmIOmL3S3Rd3YRK16or/C29vVh7+3x6epaOrHEnIiIiUg1RFyieG3MdDaNcuCumUCciIiJxiXoqFjPb18w6zeyrZraXmf2Fmc2Os7h6lUgY3d1Lym7r7l6iUCciIiKxiBTszOww4CHgIuDzYfONQCaesupbPu90dq4pu62zc82Y2bIiIiIi1RB1xO58YG/gMQB3fxG4FTg+nrLqV+ns11K9vRvLLoUiIiIiMlVRg92RQB9wQ1HbE8Cbq11QPSsX6trb57N9+5mjZssq3ImIiEgcoga73zH6HrEA7wK2Vrec+tbfv2lUqGtrm0VPz1KamhL09CwdE+76+zfVokwRERFpUFGD3W3AUuAvAczsDuBoQIsTF0mlWujqWggEI3UrVswdmShRmC1bCHddXQu1OLGIiIhUVdR17FYAC4C3hq8XEFxvd04cRdWzTGYRra2zSSabWb/+1lHbCuEulWpRqBMREZGqi7qO3ZNm9k7gBOBgYDPwY3f/fYy11a3xQlsiYQp1IiIiEovI69i5+x/c/Rp3/5q7X6tQV1kuN1RxYkQ+7+RyQ9NckYiIiMwEFYOdme2I8BiO8iFm9nozu8PM7jWzB8wsG7bva2Y3mdmj4d99ivY528yGzOwRM1ta1H6Emd0fbrvAzCxs383MrgrbbzezuZPulSnIZDaQTveVnfVamDWbTveRyWyoRXkiIiLSwMYbsbMIj6gjfi8Dx7r7u4HDgTYzOxo4C7jZ3ecBN4evMbNDgVOAw4A24Ntmtkt4rIuATmBe+GgL208Dnnf3FuDrwFcj1lY1udwQ2ewgEMx6Xbly80i4K10KJZsd1MidiIiIVNV4weyQiI8JeWBb+HLX8OFAClgVtq8C0uHzFHClu7/s7o8DQ8CRZnYA8EZ3H3R3By4r2adwrGuB4wqjedMlmWwetaTJwMBWOjpWMzycL7u+XTLZPJ3liYiISIOzIB9NwwcFI253AS3Ahe7+L2b2grvvXfSe5919HzP7FvBTd788bL+Y4BZmm4Hz3P34sP39wL+4+wlmthFoc/enwm2bgKPc/TcldXQSjPgxe/bsI6688sqqfs983lm5cjMDA5WX+GtrmzVqKZRGt23bNvbYo3QZxJlH/RBQPwTUDwH1Q0D9EFA/BCr1wzHHHHOXuy8Yb9+oy51MmbvvAA43s72BH5rZ/HHeXi7x+Djt4+1TWkc30A2wYMECX7x48ThlTM7ixZVvK9bePp+enqUzJtQBrFu3jjj6ud6oHwLqh4D6IaB+CKgfAuqHwFT6IfKs2Gpx9xeAdQTXxj0Tnl4l/Pts+LangIOKdpsDPB22zynTPmofM2sC9gKei+M7TCSRMLq7l5Td1t29ZEaFOhEREZk+0xLszOxN4UgdZrY7cDzwMHA9sCx82zIgFz6/HjglnOl6CMEkiTvcfQvwkpkdHV4/9+mSfQrHOhlY69N1nrlEPu90dq4pu62zc43uESsiIiKx2KlTsWb2euCt7v7gTn7OAcCq8Dq7BHC1u99gZoPA1WZ2GvBL4GMA7v6AmV0NPAgMA2eEp3IBTgcuBXYnuO7uxrD9YuB7ZjZEMFJ3yk7WWBWls19LFdpn2ulYERERiV+kYBeOsn2LcETMzOYBPwG+4e7fnGh/d78PaC3TvhU4rsI+5wLnlmm/ExhzfZ67/5EwGNZKuVDX3j6f7u4ldHauGWlXuBMREZE4RD0V+29Ae/h+C5cgeR74ZFyF1aP+/k2jQl1b2yx6epbS1JSgp2fpqKVQens30t+/qRZlioiISIOKGuxOJliq5KKitnuBt1W9ojqWSrXQ1bUQCEbqipc0SSRsVLjr6lqoe8aKiIhIVUW9xm4f4FbglaK23Sm/xMiMlsksorV1NslkM+vX3zpqWyHcpVItCnUiIiJSdVFH7B4mWJ7kHQBmdgbBHR8eiqes+pZKtVS8di6RMIU6ERERiUXUYHcu8Cbgg+HrC4DXA+fFUVS9y+WGKi5pks+77hErIiIisYgU7Nz9euBDwADBKN2NwIfDdimSyWwgne6jo2P1mHBXmDWbTveRyWyoUYUiIiLSqCKvY+fuq4HVMdZS93K5IbLZQSCY9bplyywWL3YSCRuzFEo2O0hr62ydlhUREZGqiTRiZ2aXVHhcHHeB9SSZbB61pMnAwFY6OlYzPJwvu75dMtlcizJFRESkQUUdsVsOOK/Ogi08d+C06pdVnwqzXoFRixGX3oWivX2+FicWERGRqosa7LJFz3cB3gl8FLik6hXVuXLhrphCnYiIiMQlUrBz92xpm5l1AwdWvaIGkEgY3d1Lyga77u4lCnUiIiISi6jX2L2l5DEf+DNgUbzl1ad83unsXFN2W2fnmopLoYiIiIhMRdRTsY9XaL+/WoU0itLZr6UK7TodKyIiItUWdYFiK3n8AfgfgkkVEioX6trb57N9+5mjZsv29m4su86diIiIyFREXaA4UfLYw93f7+73xFxfXenv3zQq1LW1zaKnZylNTQl6epaOCXf9/ZtqUaaIiIg0qKgjdpjZvmbWaWZfNbO9zOwvzGx2nMXVm1Sqha6uhUAwUrdixdyR062F2bKFcNfVtVCLE4uIiEhVRbrGzswOA9YC+4VNXya4rdhlwOnxlFafMplFtLbOJplsZv36W0dtK4S7VKpFoU5ERESqLuqI3fnA3sBjAO7+InArcHw8ZdW3VKql4sSIRMIU6kRERCQWUYPdkUAfcENR2xPAm6tdUCPI5YYqTozI551cbmiaKxIREZGZIGqw+x2wR0nbu4Ct1S2n/mUyG0in+8rOei3Mmk2n+8hkNtSoQhEREWlUUYPdbcBS4C8BzOwO4GhgfUx11aVcbohsdhAIZr2uXLl5JNyVLoWSzQ5q5E5ERESqKmqwWwFsBuYQrGO3gGDR4nPiKas+JZPNo5Y0GRjYSkfHaoaH82XXt0smm2tRpoiIiDSoqPeKfdLM3gmcABxMEPJ+7O6/j7G2ulOY9Qqv3mGit3fjmLtQtLfP150nREREpOqi3lIMd/8DcE2MtTSEcuGumEKdiIiIxCXSqVgz21HhMRx3gfUokTC6u5eU3dbdvUShTkRERGIx2XvFFj+kRD7vdHauKbuts3ON7hErIiIisYh6KvaQoue7AO8ELiRYuFiKlM5+LVVo1+lYERERqbZII3bu/kTR4zF3zwFXAH8Tb3n1pVyoa2+fz/btZ46aLdvbu7HsOnciIiIiUxH1XrFfLGl6I7AM2LXqFdWx/v5No0JdW9uskZG5crNldc9YERERqaaop2IzQPHwUuEc4hVVrabOpVItdHUtJJsdpL19PqeeutvI6dbScNfVtVChTkRERKoqarC7jNHB7nfA3cD3ql5RnctkFtHaOptkspn1628dta0Q7jRSJyIiInGIukDx8pjraCjjhbZEwhTqREREJBZRr7H7hyjvc/cLplaOiIiIiExW1FOx32D0qdhKFOxEREREaiTqAsX/TRDsngVuD/86cBuwvughQC43VHEpk3zeyeWGprkiERERmQmiBrs7gUFgjru/FzgofH2nux9TeMRVZD3JZDaQTveVXaeusM5dOt1HJrOhRhWKiIhIo4oa7DqA/3X3HQDuPgz8BjgtrsLqUS43RDY7CARLmqxcuXkk3JUuXpzNDmrkTkRERKoqarD7XyBlZjeZ2bfM7Cbgo2G7hJLJ5lF3mBgY2EpHx2qGh/Nl70iRTDbXokwRERFpUFEnT5wFfB84DjiWYIHiHWG7hCrdYaL0vrHt7fN1r1gRERGpuqjr2F1rZvcApwBvBn4FXOXuOpdYoly4K6ZQJyIiInGJOmJHGOL+PcZaGkYiYXR3Lykb7Lq7lyjUiYiISCyiXmMnOyGfdzo715Td1tm5puJSKCIiIiJToWBXZaWzX0v19m4suxSKiIiIyFQp2FVRuVDX3j6f7dvPHDVbVuFORERE4rBTwc7MXm9mh8ZVTL3r7980KtS1tc2ip2cpTU0JenqWjgl3/f2balGmiIiINKhIwc7Mdjezi4FtwH1mdoiZbTKzv4+3vPqSSrXQ1bUQCEbqVqyYOzJRojBbthDuuroWkkq11KxWERERaTxRZ8X+G9AePnd3f9zMngc+CXwzlsrqVCaziNbW2SSTzaxff+uobYVwl0q1KNSJiIhI1UU9FXsycBdwUVHbvcDbql5RA0ilWujv31T2GrpEwkgmm3U7MREREam6qMFuH+BB4JWitt0J7kAhJTKZDaTTfaPuFVtQmGCRTveRyWyoUYUiIiLSiKIGu4eBNuAdAGZ2BpAGHoqnrPqVyw2RzQ4Cr94rthDuSmfNZrODGrkTERGRqoka7M4F3gR8MHx9AfB64LwoO5vZQWZ2i5k9ZGYPmNnnwvZ9zewmM3s0/LtP0T5nm9mQmT1iZkuL2o8ws/vDbReYmYXtu5nZVWH77WY2N+J3q6pksrns0ibDw/myS6Ekk821KFNEREQaUKRg5+7XAx8CBghG6W4EPhy2RzEM/JO7vwM4GjgjXDblLOBmd58H3By+Jtx2CnAYwUjht81sl/BYFwGdwLzw0Ra2nwY87+4twNeBr0asrapKZ79CEO523fX8MaFO94wVERGRaoq8jp27r3b3j7j7fHc/wd0HdmLfLe7+8/D5SwTh8EAgBawK37aK4PQuYfuV7v6yuz8ODAFHmtkBwBvdfdDdHbisZJ/Csa4FjiuM5k23Qrhra5tVdrtCnYiIiMTBgnw0wZvMzq+w6WXgF8AP3P23kT4wOEW6HpgP/NLd9y7a9ry772Nm3wJ+6u6Xh+0XE4wSbgbOc/fjw/b3A//i7ieY2Uagzd2fCrdtAo5y99+UfH4nwYgfs2fPPuLKK6+MUvakvPjiS6TTj4xp/8lPjmCXXWZOqNu2bRt77LFHrcuoOfVDQP0QUD8E1A8B9UNA/RCo1A/HHHPMXe6+YLx9o65j94/AeAkwa2aL3f2x8Q5iZnsAPwD+0d1/O86AWrkNPk77ePuMbnDvBroBFixY4IsXLx6v5EnL552PfOTSstuuuOLlGTVit27dOuLq53qifgioHwLqh4D6IaB+CKgfAlPph6inYq8iCEn3hc/vDV/ngEeAOQSLGFdkZrsShLor3P26sPmZ8PQq4d9nw/angIOKdp8DPB22zynTPmofM2sC9gKei/j9qqow+3VgYGvZ7bpXrIiIiMQharDbDtzk7q3u/gl3fw9wE/ASwQSHW4D3Vdo5vNbtYuAhdy8+rXs9sCx8vowgKBbaTwlnuh5CMEniDnffArxkZkeHx/x0yT6FY50MrPUo55mrrHRJEwiuqdu+/cyys2UV7kRERKRaoga7k4DXlbQ1ASeF4WkdsP84+y8CPgUca2b3hI8PEyyX8kEze5RgKZXzANz9AeBqgkWRB4Az3H1HeKzTgR6CCRWbCK69gyA4zjKzIeBMwhm2062/f1PZ2a9NTYmys2X7+zfVokwRERFpQFGvsXscWBwGsEeAFoJRtEKCeQevnkYdw91vo/JdKo6rsM+5BOvnlbbfSTDxorT9j8DHKn+F6ZFKtdDVtZBsdpC2tlmjrqUrzJaFINR1dS3UPWNFRESkaqIGu9OBfqA5fAC8AJxuZm8Mj3NR+V1nnkxmEa2ts9lzzyfHTJAohLtUqkWhTkRERKoqUrBz99vCZUpOIFh/7lfADe7+YviWj8dTXv1KpVpYt+6pstsSCVOoExERkaqLOmJHGOKuMLM9CU+rmtkbo65fJyIiIiLxijR5wszmmNmPzez3BKdgnw8fNVlORERERETGijor9kKCe7K+nmC0rvghZeRyQxWXMsnnnVxuaJorEhERkUYXNdj9BfBzgnuzOnAUwVIjfxNTXXUtk9lAOt3HypWbx4S7wjp36XQfmcyGGlUoIiIijShqsPsTYBB4Jnx9P3ArcE4cRdWzXG6IbHYQgIGBraMWIS5dvDibHdTInYiIiFRN1GD3HLAH8GuC068/AE4E3hxTXXUrmWwue4eJ4eF82TtSJJPN5Q4jIiIistOiBruNwBEEa9nlgQ8B+wBrYqqrbhXWqSsNd7vuen7ZO1KUrnMnIiIiMllRlzv5EJBw91fMbDHwlwSnZb8VU111rRDutmzZwsDA1jHbFepEREQkDhOO2JlZE7Aa+L8QLFbs7v/H3c9z921xF1ivEgnj85+fW3Zbd/cShToRERGpugmDnbsPA28HDoi/nMaRzztf+9rmsts6O9dUXApFREREZLKiXmP3JSBtZh8ws13jLKgRFGa/ljsNC69OqFC4ExERkWqKGuwuAvYF1gJ/NLMd4WM4vtLqU+mSJhBcU7d9+5llZ8sq3ImIiEi1RA12MPaOE7aT+88I/f2bys5+bWpKlJ0t29+/qRZlioiISAOKGswOGechRVKpFrq6FgLQ1jZr1OzX0qVQuroWkkq11KxWERERaSyRljtx9ycAzOxtQIu7/zjWqupcJrOI1tbZ7Lnnk2NmvxbCXSrVolAnIiIiVRVpxM7M9jWznwAPAdeb2VwzGzazf4u3vPqVSrVUXNIkkTCFOhEREam6qKdiVwLHAq8A5u6bgZ8CJ8RUl4iIiIjspKjBrg1YB3ynqO1B4K3VLqhR5HJDFWe85vNOLjc0zRWJiIhIo4sa7HYHtpS07UcwgiclMpkNpNN9rFy5eUy4KyyHkk73kclsqFGFIiIi0oiiBrv7CE67HgVgZiuBJHBvTHXVrVxuiGx2EICBga2j1qorXeMumx3UyJ2IiIhUTdRg93+B3YCjCdav+ycgD2TiKat+JZPNZRciHh7Ol124OJlsrkWZIiIi0oCiLndym5ktAE4HDgY2A93ufl+MtdWlwnImwEiI6+3dOCrQwasLF1eaOSsiIiKysyIFOzM7Ceh39zNirqchFMLdli1byt4vVqFORERE4hD1VOy1wNNmdqGZHRlnQY0ikTA+//m5Zbd1dy9RqBMREZGqixrsbgX2ITgVO2hmD5vZOWb2lvhKq2/5vPO1r20uu62zc03FpVBEREREJitSsHP3Y4A3A38P/DfQAvwboDvYl1GY/VruNCy8OqFC4U5ERESqKeqIHe7+LHAJ8G1gkGB2bOT9Z4rSJU0guKZu+/Yzy86WVbgTERGRaol6r9i0mX0feBb4PrCIYMHi/4yxtrrU379pTKjr6VlKU1OCnp6lY8Jdf78GPUVERKQ6oo64XQf8Vfj+K4EPAQe5+z/HVVi9SqVa6OpaCEBb26xRs18Ls2UL4a6rayGpVEvNahUREZHGEmm5E4Lr6lYB17j7S4VGM9vH3Z+PpbI6lsksorV1Nnvu+eSY2a+FcJdKtSjUiYiISFVFnTzxAXe/xN1fMrNdzewkM/sh8HTM9dWtVKql4pImiYQp1ImIiEjVRZ78YGbvN7PvAs8A1wAp4HVxFVbvcrmhihMj8nnXPWJFRESk6sYNdmb2Z2b272b2GLAO6AD2JpgR+wvgmLgLrEeZzAbS6T5Wrtw8JtwVZs2m031kMhtqVKGIiIg0oolG7B4CzgbmAi8AlwMnhdsedPf1sVVWp3K5IbLZQQAGBraOWtKkdCmUbHZQI3ciIiJSNVFPxf4cOMndl7l7X4z11L1ksrnsenXDw/my69slk821KFNEREQa0ESzYn8JvAVoBdaa2TPADbFXVccKs16BkRDX27txVKCDV9e30z1jRUREpFrGHbFz97nAYoI7TrwI/ClwGuDAMWb2lZjrq0uFcNfWNqvsdoU6ERERicOEp2Ldfb27f4Yg1J0MXA9sB/YCtEBxBYmE8fnPzy27rbt7iUKdiIiIVN3O3Cv2FXe/zt1PJAh5pwO3xVZZncvnna99bXPZbZ2da3SPWBEREam6yMGumLu/4O7fdfcPVLugRlCY/TowsLXs9sKECoU7ERERqaZJBTuprHRJEwiuqdu+/cyys2UV7kRERKRaFOyqrL9/05hQ19OzlKamBD09S8eEu/7+TbUoU0RERBqQgl2VpVItdHUtBKCtbdao2a+F2bKFcNfVtVD3jBUREZGqmWgdO5mETGYRra2z2XPPJ8fMfi2Eu1SqRaFOREREqkojdjFJpVoqLmmSSJhCnYiIiFSdgp2IiIhIg1Cwi9Fttz1fcdZrPu/kckPTXJGIiIg0MgW7mGQyG/jCFzaVXdKksCRKOt1HJrOhRhWKiIhIo5mWYGdml5jZs2a2sahtXzO7ycweDf/uU7TtbDMbMrNHzGxpUfsRZnZ/uO0CM7OwfTczuypsv93M5k7H96oklxsimx0Exq5XV7rOXTY7qJE7ERERqYrpGrG7FGgraTsLuNnd5wE3h68xs0OBU4DDwn2+bWa7hPtcBHQC88JH4ZinAc+7ewvwdeCrsX2TCJLJ5rKLEQ8P58suXpxMNteiTBEREWkw0xLs3H098FxJcwpYFT5fBaSL2q9095fd/XFgCDjSzA4A3ujug+7uwGUl+xSOdS1wXGE0rxYKS5q0tc0aaevt3ciuu55fdvHiSrNnRURERHZGLa+xm+3uWwDCv/uH7QcCTxa976mw7cDweWn7qH3cfRh4EZhFDSUSxooVc0eN3BVTqBMREZFqey0uUFwu6fg47ePtM/bgZp0Ep3OZPXs269atm0SJ0fz+97/jk598A729Y7d98pO7sX79rbF99mvJtm3bYu3neqF+CKgfAuqHgPohoH4IqB8CU+mHWga7Z8zsAHffEp5mfTZsfwo4qOh9c4Cnw/Y5ZdqL93nKzJqAvRh76hcAd+8GugEWLFjgixcvrs63KWPt2lu4/PKXy2674oqXZ8yI3bp164izn+uF+iGgfgioHwLqh4D6IaB+CEylH2p5KvZ6YFn4fBmQK2o/JZzpegjBJIk7wtO1L5nZ0eH1c58u2adwrJOBteF1eDWTzzsrV24edU1dsdLZsiIiIiJTNV3LnXwfGAT+zMyeMrPTgPOAD5rZo8AHw9e4+wPA1cCDwABwhrvvCA91OtBDMKFiE3Bj2H4xMMvMhoAzCWfY1kphSZOBga0jbe3t89m+/cyys2UV7kRERKQapuVUrLv/dYVNx1V4/7nAuWXa7wTGzEZw9z8CH5tKjdXU37+p4uzXnp5gWb7C9t7ejaRSLbp3rIiIiEyZ7jwRg1Sqha6uhcDY2a+FcFcYuevqWqhQJyIiIlXxWpwV2xAymUU0NT3LOeeMnSBRCHcaqRMREZFq0ohdjN73vn0qznpNJEyhTkRERKpKwU5ERESkQSjYxei2256vOOM1n3dyuaFprkhEREQamYJdTDKZDXzhC5vKLmdSWA4lne4jk9lQowpFRESk0SjYxSCXGyKbHQTGrlVXCHWF5U6y2UGN3ImIiEhVKNjFIJlsLrsQ8fBwflSog2A5lGSyuRZlioiISIPRcicxKCxnsmXLlpG7T/T2bhxze7HSNe5EREREpkIjdjFJJIwVK+aOGrkrplAnIiIi1aZgF6NEwujuXlJ2W3f3EoU6ERERqSoFuxjl805n55qy2zo711RcCkVERERkMnSNXUzyeWflys0j19iVKlxvp9OxIiIiUi0asYtBYUmT4lDX3j6f7dvPLDtbViN3IiIiUg0KdjHo7980ZkmTnp6lNDUl6OlZOibc9fdvqkWZIiIi0mAU7GKQSrXQ1bUQGDv7tbAUSiHcdXUtJJVqqVmtIiIi0jh0jV1MMplFNDU9yznnjL2GrhDuUqkWhToRERGpGo3Yxeh979un4sSIRMIU6kRERKSqFOxilssNVZwckc+77hMrIiIiVaNgF6NLL/0V6XRf2ZmvhZmz6XQfmcyGGlUoIiIijUTBLia53BCrVm0Bxi5rUgh1hZmz2eygRu5ERERkyhTsYpJMNtPWNmvkdSHcDQ/nR4U6CGbOJpPNtShTREREGohmxcYkkTBWrJjLAQccMBLiens3jgp0MHY5FBEREZHJ0ohdjErXrCulUCciIiLVpGAXs0TC6O5eUnZbd/cShToRERGpGgW7mOXzTmfnmrLbOjvX6D6xIiIiUjUKdjEqnf1aqnS2rIiIiMhUKNjFJJ93Vq7cPGb26/btZ4665k7hTkRERKpFwS4m/f2bGBjYOvK6MFGiqSkxZkJFb+9G+vs31aJMERERaSAKdjFJpVpYtuwAYOzs19LZsl1dC3XfWBEREZkyrWMXo+XLD+TEE48imWweM/u1EO5SqRaFOhEREakKBbuYjRfaEglTqBMREZGq0alYERERkQahYDdNcrmhijNf83knlxua5opERESk0SjYTYNMZgPpdF/ZZU0Ka92l031kMhtqVKGIiIg0AgW7mOVyQ2Szg8DYNetKFzDOZgc1ciciIiKTpmAXs2SyecyadaedNsDwcH7MXSmWLz9MCxWLiIjIpCnYxax0zTqASy99gF13PX9MqAM46aScTsmKiIjIpCjYTYNEwkgmmytuL4S6Sy99ANApWREREZkcBbtpEtyJ4rCy29xfDXUQ3KlivCAoIiIiUo6C3TQyK9++atXoUFd8+zERERGRqBTspkFh9mvxqFw5y5cfRnf3Evr7N01TZSLVlbsnRz6fH/lbbKTdg78iIlJ9CnYxK13SZDzu8JnPaE07qU+Z6zOkL0zznn97D+kL03Rc1jES7vL5PKetOo30hWn+9sa/JX1hmsz1mVqWKyLSkHSv2Jj192+KFOpg9CnZbHaQ1tbZupes1IXcPTmy/VkA7n3qXgB6N/TyxNYnuPHvb+Rvr/hbLv2fSwEYej6YGJTtz/LK8Ct8+aQv16RmEZFGpBG7mKVSLXR1LQRg2bLDaGnZK9J+mkAh9aT0tGvB2ofXstc/7jUS6kp95cavcEr3KSOnaUVEZGoU7KZBJrOI665LYQZDQy9O+P558/amu3uJJlBI3UgdnmL5e5eX3fbH7X8cd9+rfnYVLf/aotOzIiJVoFOx0ySRsFGTJ+bN25tHH32h7HsfffQFfvSjx3QaVupGIpHg4mUXA1QcnRvP4795HAhOz777oHePPb4lSB2emlKNIiIzgYLdNCmcks1mB2lvn893vvNBdtvt62Xf29W1UKFO6k4h3DnOqv9ZNaljLH7bYi74yQWs+8W6Mds+dsTHaN6/mSMPOZLUu1Pk7s3xs8d/xpc++iV+tPFHJN+VpP++/pEAmM/nR70WEZkJdCp2GmUyi+jrS9PdvYS/+7ubyr7n2GPfwhe/+N5prkzktWHdL9aVDXUA19x1DefdeB4nffskWr/UyknfPomv3PgVZn9+NukL0xzx70eQvjDNKd2nMDw8TMdlHaQvTNOV6xo5RuFavtw9OYaHh8te1zfe9X7llnEptI93vHOuO6fidYjlPq/S50xUXyWlxyt+XXq84teTrSPqfoXlb3b2+Dv7OXGbah1T7Ye465uqWn9+XF6r30vBbpolk810dq6pOFN27dpf0tGxmnzep7kykakpLGky2dG6nXHfr+4bef7c754D4J4n7wGCa/bectZb6N3QC8CXbvgSP7z7h+Tz+ZGwl74wzaFdh465rq/4PaXX+xWWcylexqW4vdLxjvj3I/jKjV/hiH8/ouzafqWfV+lzJqqvktLjFb8uDsCZ6zOjjr945eJJ1RG1/sLxV/505aS+Z7X7abKmWkdh/8n2Q9z1TVWtPz8ur+XvZe4zN0AsWLDA77zzztiOv27dOhYvXjzyutyadu3t8+nuXjIm7DXSHShK+2GmauR+KIS6yVxfNx2WLVyGmVWsr++MPpLvStJxWcdIICy0pw5PkbsnR/rC9Eh7+6J2ej7dQ/99/aPaS4/3wa9/kLUPrx1pP+7tx7Hm/6whkUiw9pa1XP7E5aM+7+wPnc1XbvzKmM9JJBIj/2dRrr5KSus+9u3Hjqpn3v7zePTZR0fVd/PDN485TtQ6KvVTpf0m+z139nMm6qfJmmodcX+PWvfTZD5/rxf2es3/Ozkd/Vrp/y/M7C53XzDevg01YmdmbWb2iJkNmdlZta6nVOmadoXw1tSUoKdnKe3t80e29fZu1B0opG7k7s29ZkMdwKrBVRXrm7f/PD502IfG/GPcvqid5LuSACTflaR9UfvItt4NvXRc1sGHDvsQ8/afV/F4xSEK4OaHbw5GynYMs/KnK8d83pc++qWynzO8Y3jc+ioprXvtw2tH1Vsc6ubtP29UqCt+X9Q6KvVTuf0mc/xK32uq/TRZU60j7u9R636q9efH5bX+vRpmxM7MdgF+AXwQeAr4GfDX7v5gpX2me8QOIJPZMDKBonRErnhEr6trIZnMothqm06NPFK1Mxq5H0r/C7beFf8XeMF4I04TKR0ZG+/zonxOufoqmUzd7Yva6T61m87LO3e6jqj1T/b4O/s5UftpsqZaR9zfo9b9tLOfXy//TsbdrxqxCxwJDLn7Y+7+CnAl8JqbDleYQFHuNGsiYfT0LKWvL90woU5mhtThKbqSwSSFY99+bI2riaZ0pK2g0j/GiUSCnk/3jPov9ajHezD7YMX9Sj9vos/Z2f+zmOh4lY7f1NQ0qTqi1l84fttb23bq+Dv7OXGGumrUUdh/sv0Qd31TVevPj8tr+Xs10ojdyUCbu3eErz8FHOXuny15XyfQCTB79uwjrrzyythq2rZtG3vssUdsx68X6ofATOiH2568jffOeS+X3X8Zq+4vP4ni2DnH8tBzD7Hl91umubrRVv/VapZetXRM+0/++ifsktil4n478js4/vvH7/TxKu1X6fN29v0TqXS8iY4/2Tqi7vfib18k3Z/e6eNPtb5qm2odU+2HuOubrs+vt38n4+rXSv1wzDHHTDhi10jr2JWbZTAmtbp7N9ANwanYOId862VIOW7qh8BM6IfFLAbg2GOO5cR7TuS/bv8vrr7zag4/6HDuefIelr93OVu2bKl5qAP47C2fLdt+xS+vmPC02c4er3DaMernjfc549VXyXjHG+/4k60j6n75fJ6PfPUjO338nf2cuE21jqn2Q9z1TdXOfH49/TsZZ79OpR8aKdg9BRxU9HoO8HSNahGZ8VKHp0gdnuITR31iZPHgfD7PSf9zUqyf+8bXv5Hf/vG3E76v0jVvhWtmdvbasfGOd9ujt0X+vIk+p1J9lezsNXaF9010Ddxk+6n0+AOPDezU8Xf2c2p9jV3U7zHZfoi7vqmq9efH5bX8veqnFyf2M2CemR1iZq8DTgGur3FNIjNe6vAUiURwS7AT33Miy965LNbPixLqis3bfx4vf/vlsrPcihfxLTfb7eVvv1x2Vmzp8YpDXfuidrZ/Z/uoa6pGZtUNl59Vt/0728etr5JydVe6FrB0luqhXYfudB2V+qncfpM5/njfayr9NFlTrSPu71Hrfqr158fltf69GibYufsw8FlgNfAQcLW7PzD+XiIy3Za/azl9Z/Rx3enXjTw+vuDjo94zd9bckecHzzp4zDHedeC7Rp7v+4Z9AThkv0Mqf+Z7l7P8vcvLbnv02Ue58YEbx1wI3buhl/77+gHov69/zD/iPZ/u4cYHbhwzEld8vNKJJMe9/bhg4sAuTaw4esWYz/vi9V8s+zlNu4ydyFBcXyWldR/79mPHLHFSXPdxbz9u1OudraNSP5XbbzLHr/S9ptpPkzXVOuL+HrXup1p/flxe89/L3Wfs44gjjvA43XLLLbEev16oHwLqh0Clfui7u8+vu+s6v+6u63zHjh0jr3fs2OHX3XWdX3vXtX7WD87y634etv38Oj/7B2f79u3bve/uPt+xY4f/1Xf/yunA23vb/Qs//MLI8x07dviOHTu8vbfd6cDpwOedM8/pwLtyXSM1FL+nuN3dvSvXNep4pe2Vjnd49nCnAz88e/io/W655Zayn1fpcyaqr5LS4xW/3r59+6jjFR//A//xgUnVEbX+wvHbvtw2qe9Z7X6arKnWUdh/sv0Qd31TtbOfXy//Tsbdr5X6AbjTJ8g2NQ9XtXwo2E0P9UNA/RCIux8KIa/0ubuPBMa+u/tGAmGpwnsmOnZp+3jHO/sHZ4/Zr9AP5T6v0udMVF8lpccrfl16vOLXk60j6n59d/f5zWtv3unj7+znxG2qdUy1H+Kub6p25vPr6d/JOPt1KsGuYZY7mYxaLFA8E6kfAuqHgPohoH4IqB8C6oeA+iGgBYpFRERERMFOREREpFEo2ImIiIg0CAU7ERERkQahYCciIiLSIBTsRERERBqEgp2IiIhIg5jR69iZ2f8CT8T4EfsBv4nx+PVC/RBQPwTUDwH1Q0D9EFA/BNQPgUr9cLC7v2m8HWd0sIubmd050UKCM4H6IaB+CKgfAuqHgPohoH4IqB8CU+kHnYoVERERaRAKdiIiIiINQsEuXt21LuA1Qv0QUD8E1A8B9UNA/RBQPwTUD4FJ94OusRMRERFpEBqxExEREWkQCnZTZGZtZvaImQ2Z2VlltpuZXRBuv8/M3lOLOuMWoR8Wm9mLZnZP+PhiLeqMm5ldYmbPmtnGCttnyu9hon6YKb+Hg8zsFjN7yMweMLPPlXlPw/8mIvZDw/8mzOz1ZnaHmd0b9kO2zHtmwu8hSj80/O8BwMx2MbO7zeyGMtsm91twdz0m+QB2ATYBbwVeB9wLHFryng8DNwIGHA3cXuu6a9QPi4Ebal3rNPTFXwDvATZW2N7wv4eI/TBTfg8HAO8Jn+8J/GKG/hsRpR8a/jcR/m+8R/h8V+B24OgZ+HuI0g8N/3sIv+eZwH+V+66T/S1oxG5qjgSG3P0xd38FuBJIlbwnBVzmgZ8Ce5vZAdNdaMyi9MOM4O7rgefGectM+D1E6YcZwd23uPvPw+cvAQ8BB5a8reF/ExH7oeGF/xtvC1/uGj5KL3SfCb+HKP3Q8MxsDvARoKfCWyb1W1Cwm5oDgSeLXj/F2H+soryn3kX9jgvDofcbzeyw6SntNWcm/B6imlG/BzObC7QSjE4Um1G/iXH6AWbAbyI89XYP8Cxwk7vPyN9DhH6Axv89fAP4ZyBfYfukfgsKdlNjZdpK/6sjynvqXZTv+HOCW6G8G/gm0Bd3Ua9RM+H3EMWM+j2Y2R7AD4B/dPfflm4us0tD/iYm6IcZ8Ztw9x3ufjgwBzjSzOaXvGVG/B4i9END/x7M7ATgWXe/a7y3lWmb8LegYDc1TwEHFb2eAzw9iffUuwm/o7v/tjD07u4/BnY1s/2mr8TXjJnwe5jQTPo9mNmuBGHmCne/rsxbZsRvYqJ+mEm/CQB3fwFYB7SVbJoRv4eCSv0wA34Pi4CPmtlmgsuXjjWzy0veM6nfgoLd1PwMmGdmh5jZ64BTgOtL3nM98OlwdsvRwIvuvmW6C43ZhP1gZn9qZhY+P5Lgt7d12iutvZnwe5jQTPk9hN/xYuAhdz+/wtsa/jcRpR9mwm/CzN5kZnuHz3cHjgceLnnbTPg9TNgPjf57cPez3X2Ou88l+P/Mte5+asnbJvVbaKp+uTOHuw+b2WeB1QQzQy9x9wfM7O/C7d8Bfkwws2UI+D3QXqt64xKxH04GTjezYeAPwCkeTvtpJGb2fYLZXPuZ2VNAF8GFwTPm9wCR+mFG/B4I/qv8U8D94fVEAOcAb4EZ9ZuI0g8z4TdxALDKzHYhCCpXu/sNM+3/M4jWDzPh9zBGNX4LuvOEiIiISIPQqVgRERGRBqFgJyIiItIgFOxEREREGoSCnYiIiEiDULATERERaRAKdiIiIiINQsFOROpGuFDnZjPz8PGOWtdUb8wsE/bdpbWuRUSqT8FOROrJXwAHF73+VJwfFt4GS0SkbijYiUg9Kdxy5+7w7yeKbjt0azgSdVLhzWZ2S9h2cvj6fWa2zsyeN7OnzewSM5sVbptbNBL4d2b2NLDGzHY1s5vM7Ndm9oqZvWBm15vZQUWf8z4zu9/Mfmdm3zOzK8PjfKPoPR81szvM7Ldm9oSZ/aeZ/UmlL2pm7zCzH4Z1/sHM7jGzg4tqvcbMtoTf5RYzO6po30+Y2YPhfs+Z2WBYY4bgLiAAy8Ia1032fwwRee3RLcVEpC6Y2W4EtxkC+CeCG8ofTDCKdytwWfj8r4DrzGx2+Pp5oN/M5gM3A68ANxDc1qgdmGtmx5V83LlAH/Brgv8APoDglnnbgIVAEngd0Bbe87If2JvgZub7E9z7srj2pUAO+E3491DgTGBfytwmyMz+FPhvYBZBiP0RcCSwj5n9BlgLHAKsD495ErDWzN5FcJPwS4HtwBXAbsB7gGbgp8DtwFHAQ8AagtsViUiDULATkXpxAkF4epYgyN1AcCr21PD1NcA3gRPM7A0EIbBwH8qXzex0gjB2N/BM+DgaOAb4M+CPRZ/1MXdfW3hhZicShLk/Be4HWoHFZpYoqusx4Fh39/B+qO8uOt4/hH/vJriR+e0EYWuZmZ3h7r8v+a6nEoS6e4AF7p4P62giCHGHhJ+3OPy8HwJp4DTgywT3bH6WIJw+6O6Pmdku7r4jvJn4UcAd7v6P43W4iNQfBTsRqReF07D97p4Pw8yngI+Z2Wfd/bdm1gf8NUHY+nj4/lXh37nh36PCR7EWYGPR6w2FJ2b2fuAWgrBUbDdgT+DA8PUjRTcpf4jRwa7w2R8MHyOHB95a8tkQBDcIwle+0Ojuw2ZWOFbx5z0c/j3Y3beFIbaLYCQRM3uKoK/WISINTdfYichrnpntA3w4fHmamTlwXfh6L4LRNAhOxwL8PfA+4FF3HwzbNod/z3d3KzyAt7r7DcWf5+4vF738S4JQNwC8gdGh0IBfhc9bitrfXvIVCp/9DyWf3ezupaEO4PHw75+Ho4LBhwUjdoVjva1wfSHBiCPAE+HfVe5+IPBm4HPAHOAL4bYd4V/9+y/SgDRiJyL14OMEp1F/SzB6VnAoMI9gNOpa4CZgC7Ao3P69ovd2A58BPmdmbyW4Nu0dwHsZP+Q8E/49iuBU7wdKtt8AvADMM7OfAMPAu0re8y2CYPofZvZe4A/he2bx6uhcscuBswhO+d5hZncBRwAdBNfbbSa4Zu6W8Jq7E8NjXlKoOZwU8TTwzrDthfDvk+HfD5nZN4F17v6Dcb6/iNQR/RebiNSDT4Z/v+vu6cKDIKhBEFJmufsOggkDAE5RsHP3ewkmNawnmFRxCsGp1PMm+OxvEVyrtlu437nFG939BYIRw40EEyv+F7g+3Pxy+J4bCcLXvQQB7yQgD/y/ch/o7r8G3h9+7oHApwn+Q/x5d/8dcBzB5JG3h9/pVuA4dy9MhLiJ4Bq+04DDCMLgP4XbriGYCPIG4LME1xiKSIOwVy/REBGRyTCzvdz9xfB5AniAIHR1uPvFNS1ORGYUBTsRkSkys2sITsE+RHCq9liC06CHhSN6IiLTQqdiRUSm7ucEkzX+FXgbcBXwAYU6EZluGrETERERaRAasRMRERFpEAp2IiIiIg1CwU5ERESkQSjYiYiIiDQIBTsRERGRBqFgJyIiItIg/j/6/kFIB3QLggAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure( figsize=(10,6) ) \n",
    "\n",
    "# C = 0 Case\n",
    "\n",
    "# C = Inf/Fluid Case\n",
    "# ylim = max( max( average_queue_B ), max( average_queue_M ) )\n",
    "\n",
    "# plt.plot([fluid_sol['Cost'],fluid_sol['Cost']],[0,ylim],linewidth = 3)\n",
    "# Batching data\n",
    "plt.plot(average_cost_B2,average_queue_B2,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "plt.plot(average_cost_B,average_queue_B,'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkgreen\")\n",
    "# Max Weight data\n",
    "# plt.plot(average_cost_M, average_queue_M,'go',markersize = 8)\n",
    "# plt.plot([Ex],[1],'r*',markersize = 12, markeredgewidth=3)\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "# plt.legend(['Fluid', 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "# plt.legend([ 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "file_name = \"../longest_spatial_uniform_25_all_good.pkl\"\n",
    "with open(file_name,'rb') as f:\n",
    "        M_res,B_res, N, W, pmf_cust, pmf_serv = pickle.load(f)\n",
    "Q_paths_M = M_res[\"Q_paths\"]\n",
    "C_paths_M = M_res[\"C_paths\"]\n",
    "Q_paths_B = B_res[\"Q_paths\"]\n",
    "C_paths_B = B_res[\"C_paths\"]\n",
    "(average_cost_M, average_queue_M) = utils.average_paths(C_paths_M,Q_paths_M)\n",
    "(average_cost_B, average_queue_B) = utils.average_paths(C_paths_B,Q_paths_B)\n",
    "\n",
    "plt.figure( figsize=(10,6) ) \n",
    "\n",
    "# C = 0 Case\n",
    "\n",
    "# C = Inf/Fluid Case\n",
    "# ylim = max( max( average_queue_B ), max( average_queue_M ) )\n",
    "\n",
    "# plt.plot([fluid_sol['Cost'],fluid_sol['Cost']],[0,ylim],linewidth = 3)\n",
    "# Batching data\n",
    "plt.plot(np.log(average_cost_B2-Cstar),np.log(average_queue_B2),'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkblue\")\n",
    "plt.plot(np.log(average_cost_B-Cstar),np.log(average_queue_B),'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkgreen\")\n",
    "# Max Weight data\n",
    "# plt.plot(average_cost_M, average_queue_M,'go',markersize = 8)\n",
    "# plt.plot([Ex],[1],'r*',markersize = 12, markeredgewidth=3)\n",
    "plt.ylabel(\"Average queue length\", weight='bold',fontsize=12)\n",
    "plt.xlabel(\"Average cost\", weight='bold',fontsize=12)\n",
    "plt.title(\"c vs q\", weight='bold',fontsize=15)\n",
    "# plt.legend(['Fluid', 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "# plt.legend([ 'Batching', 'Max-weight', 'c = 0 sol'])\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x18f20660518>]"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.log(average_cost_B-Cstar),np.log(average_queue_B),'x',markersize = 10, markeredgewidth=3, markeredgecolor=\"darkgreen\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Batching 3D change it to different notebook later"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ -9  -9  -7]\n",
      "  [-12 -12 -12]\n",
      "  [-15 -15 -15]]\n",
      "\n",
      " [[ -6  -6  -4]\n",
      "  [ -9  -9  -9]\n",
      "  [-12 -12 -12]]\n",
      "\n",
      " [[ -3  -3  -1]\n",
      "  [ -6  -6  -6]\n",
      "  [ -9  -9  -9]]]\n",
      "Distance between [1, 2, 3] and [10, 11, 10]: 14.53\n",
      "Distance between [1, 2, 3] and [13, 14, 15]: 20.78\n",
      "Distance between [1, 2, 3] and [16, 17, 18]: 25.98\n",
      "Distance between [4, 5, 6] and [10, 11, 10]: 9.38\n",
      "Distance between [4, 5, 6] and [13, 14, 15]: 15.59\n",
      "Distance between [4, 5, 6] and [16, 17, 18]: 20.78\n",
      "Distance between [7, 8, 9] and [10, 11, 10]: 4.36\n",
      "Distance between [7, 8, 9] and [13, 14, 15]: 10.39\n",
      "Distance between [7, 8, 9] and [16, 17, 18]: 15.59\n"
     ]
    }
   ],
   "source": [
    "def calculate_distances(list1, list2):\n",
    "    # Convert lists to numpy arrays\n",
    "    arr1 = np.array(list1)\n",
    "    arr2 = np.array(list2)\n",
    "    \n",
    "    # Use broadcasting to calculate differences\n",
    "    diff = arr1[:, np.newaxis, :] - arr2[np.newaxis, :, :]\n",
    "    print(diff)\n",
    "    # Calculate Euclidean distances\n",
    "    distances = np.sqrt(np.sum(diff**2, axis=2))\n",
    "    \n",
    "    return distances\n",
    "\n",
    "# Example usage\n",
    "coordinates1 = [[1, 2, 3], [4, 5245, 6], [7, 8, 9]]\n",
    "coordinates2 = [[10, 11, 10], [13, 14, 15], [16, 17, 18]]\n",
    "\n",
    "results = calculate_distances(coordinates1, coordinates2)\n",
    "\n",
    "for i, coord1 in enumerate(coordinates1):\n",
    "    for j, coord2 in enumerate(coordinates2):\n",
    "        print(f\"Distance between {coord1} and {coord2}: {results[i, j]:.2f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.12450235 1.58299011 0.95801632]\n",
      " [0.9394784  1.03280478 1.31869172]\n",
      " [0.88815541 1.38633744 1.42111603]]\n"
     ]
    }
   ],
   "source": [
    "grid_size = 2\n",
    "time_steps = 6\n",
    "Tbatch = 3\n",
    "from scipy.optimize import linear_sum_assignment\n",
    "\n",
    "cust_arrivals_x = np.random.uniform(low=0, high=grid_size, size=time_steps)\n",
    "cust_arrivals_y = np.random.uniform(low=0, high=grid_size, size=time_steps)\n",
    "cust_arrivals_z = np.random.uniform(low=0, high=grid_size, size=time_steps)\n",
    "# cust_arrivals = np.column_stack((x_coords, y_coords))\n",
    "serv_arrivals_x = np.random.uniform(low=0, high=grid_size, size=time_steps)\n",
    "serv_arrivals_y = np.random.uniform(low=0, high=grid_size, size=time_steps)\n",
    "serv_arrivals_z = np.random.uniform(low=0, high=grid_size, size=time_steps)\n",
    "\n",
    "customers = []\n",
    "servers = []\n",
    "\n",
    "customers.append([cust_arrivals_x[0],cust_arrivals_y[0],cust_arrivals_z[0]])\n",
    "servers.append([serv_arrivals_x[0],serv_arrivals_y[0],serv_arrivals_z[0]])\n",
    "for k in range(1,time_steps):\n",
    "\n",
    "    queue_length = len(customers)\n",
    "    W = np.zeros(shape=(queue_length,queue_length))\n",
    "    matching_cost = 0\n",
    "\n",
    "    # Batching\n",
    "    if k%Tbatch == 0:\n",
    "        coords1 = np.array(customers)\n",
    "        coords2 = np.array(servers)\n",
    "        diff = coords1[:, np.newaxis, :] - coords2[np.newaxis, :, :]\n",
    "        W = np.sqrt(np.sum(diff**2, axis=-1))\n",
    "        print(W)\n",
    "        row_ind, col_ind = linear_sum_assignment(W)\n",
    "        matching_cost = W[row_ind,col_ind].sum()\n",
    "        customers = []\n",
    "        servers = []\n",
    "\n",
    "    customers.append([cust_arrivals_x[k],cust_arrivals_y[k],cust_arrivals_z[k]])\n",
    "    servers.append([serv_arrivals_x[k],serv_arrivals_y[k],serv_arrivals_z[k]])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.93477947  0.32184863 -0.53582306]\n",
      "[ 1.02324401 -1.00732437 -0.66642854]\n",
      "[ 0.16849222  0.19418563 -0.92287463]\n",
      "[ 0.14140926  0.67663439 -0.63623029]\n",
      "[ 0.22987381 -0.65253861 -0.76683578]\n",
      "[-0.62487798  0.54897139 -1.02328187]\n",
      "[ 0.04860966  0.33174868 -0.82243537]\n",
      "[ 0.13707421 -0.99742432 -0.95304086]\n",
      "[-0.71767758  0.20408568 -1.20948695]\n"
     ]
    }
   ],
   "source": [
    "for coord in coords1:\n",
    "    for coord2 in coords2:\n",
    "        print(coord-coord2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 0.93477947  0.32184863 -0.53582306]\n",
      "  [ 1.02324401 -1.00732437 -0.66642854]\n",
      "  [ 0.16849222  0.19418563 -0.92287463]]\n",
      "\n",
      " [[ 0.14140926  0.67663439 -0.63623029]\n",
      "  [ 0.22987381 -0.65253861 -0.76683578]\n",
      "  [-0.62487798  0.54897139 -1.02328187]]\n",
      "\n",
      " [[ 0.04860966  0.33174868 -0.82243537]\n",
      "  [ 0.13707421 -0.99742432 -0.95304086]\n",
      "  [-0.71767758  0.20408568 -1.20948695]]]\n"
     ]
    }
   ],
   "source": [
    "print(diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.12450235 1.58299011 0.95801632]\n",
      " [0.9394784  1.03280478 1.31869172]\n",
      " [0.88815541 1.38633744 1.42111603]]\n"
     ]
    }
   ],
   "source": [
    "print(np.sqrt(np.sum(diff**2, axis=-1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1245023492919126\n",
      "1.582990111391642\n",
      "0.9580163213929124\n",
      "0.9394783962315584\n",
      "1.0328047790764179\n",
      "1.318691723440388\n",
      "0.8881554072924821\n",
      "1.3863374368122172\n",
      "1.4211160264518543\n"
     ]
    }
   ],
   "source": [
    "vals = []\n",
    "for coord in coords1:\n",
    "    for coord2 in coords2:\n",
    "        print(np.sqrt(np.sum((coord-coord2)**2)))\n",
    "        vals.append(np.sqrt(np.sum((coord-coord2)**2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1, 0], dtype=int64)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col_ind"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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